<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><Version>2.2.0.25</Version><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><ReportLongName>006100 - Disclosure - Short-Term Debt and Credit Facility</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelColumn>false</LabelColumn><CurrencyCode>USD</CurrencyCode><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName>1/1/2010 - 12/31/2010
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DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: Times New Roman; FONT-SIZE: 12pt; FONT-WEIGHT: bold"&gt;10.&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;Short-Term Debt and Credit Facility&lt;/font&gt;&lt;/div&gt;&lt;div style="TEXT-INDENT: 0pt; DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&amp;#160;&lt;/div&gt;&lt;div style="TEXT-INDENT: 40pt; DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: Times New Roman; FONT-SIZE: 12pt"&gt;At December 31, 2010 and 2009, there were $68.9 million and $125.9 million, respectively, in net outstanding advances to OGE Energy.&amp;#160;&amp;#160;The Company has an intercompany borrowing agreement with OGE Energy whereby the Company has access to up to $250 million of OGE Energy&amp;#8217;s revolving credit amount.&amp;#160;&amp;#160;This agreement has a termination date of January 9, 2012.&amp;#160;&amp;#160;At December 31, 2010, there were no intercompany borrowings under this agreement.&amp;#160;&amp;#160;The Company also has $389.0 million of liquidity under a bank facility which is available to back up the Company&amp;#8217;s commercial paper borrowings and to provide revolving credit borrowings.&amp;#160;&amp;#160;This bank facility can also be used as a letter of credit facility. At December 31, 2010, there was $0.3 million supporting letters of credit at a weighted-average interest rate of 0.33 percent.&amp;#160;&amp;#160;There were no outstanding borrowings under this revolving credit agreement and no outstanding commercial paper borrowings at December 31, 2010.&amp;#160;&amp;#160;At December 31, 2010, the Company had less than $0.1 million in cash and cash equivalents.&lt;/font&gt;&lt;/div&gt;&lt;div style="TEXT-INDENT: 0pt; DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&amp;#160;&lt;/div&gt;&lt;div style="TEXT-INDENT: 40pt; DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: Times New Roman; FONT-SIZE: 12pt"&gt;OGE Energy&amp;#8217;s and the Company&amp;#8217;s ability to access the commercial paper market could be adversely impacted by a credit ratings downgrade or major market disruptions.&amp;#160;&amp;#160;Pricing grids associated with OGE Energy&amp;#8217;s and the Company&amp;#8217;s credit facilities could cause annual fees and borrowing rates to increase if an adverse ratings impact occurs.&amp;#160;&amp;#160;The impact of any future downgrade could include an increase in the cost of OGE Energy&amp;#8217;s and the Company&amp;#8217;s short-term borrowings, but a reduction in OGE Energy&amp;#8217;s and the Company&amp;#8217;s credit ratings would not result in any defaults or accelerations. Any future downgrade of the Company could also lead to higher long-term borrowing costs and, if below investment grade, would require the Company to post cash collateral or letters of credit.&lt;/font&gt;&lt;/div&gt;&lt;div style="TEXT-INDENT: 0pt; DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&amp;#160;&lt;/div&gt;&lt;div style="TEXT-INDENT: 40pt; DISPLAY: block; MARGIN-LEFT: 0pt; MARGIN-RIGHT: 0pt" align="justify"&gt;&lt;font style="DISPLAY: inline; FONT-FAMILY: Times New Roman; FONT-SIZE: 12pt"&gt;Unlike OGE Energy, the Company must obtain regulatory approval from the FERC in order to borrow on a short-term basis.&amp;#160;&amp;#160;The Company has the necessary regulatory approvals to incur up to $800 million in short-term borrowings at any one time for a two-year period beginning January 1, 2011 and ending December 31, 2012.&lt;/font&gt;&lt;/div&gt;</NonNumbericText><NonNumericTextHeader>10.&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;Short-Term Debt and Credit Facility&amp;#160;At December 31, 2010 and 2009, there were $68.9</NonNumericTextHeader><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>us-types:textBlockItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>This element may be used as a single block of text to encapsulate the entire disclosure for short-term borrowings including data and tables.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Regulation S-X (SX)
 -Number 210
 -Section 03
 -Paragraph 16
 -Article 7

Reference 2: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Regulation S-X (SX)
 -Number 210
 -Section 02
 -Paragraph 19
 -Article 5

Reference 3: http://www.xbrl.org/2003/role/presentationRef
 -Publisher SEC
 -Name Regulation S-X (SX)
 -Number 210
 -Section 03
 -Paragraph 13
 -Article 9

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