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Exhibit 5.1

July 28, 2014

Independence Contract Drilling, Inc.

11601 North Galayda Street

Houston, Texas 77086

RE: Independence Contract Drilling, Inc. Registration Statement on Form S-1

Ladies and Gentlemen:

We have acted as counsel to Independence Contract Drilling, Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing of its Registration Statement on Form S-1 (Registration No. 333-196914), as amended and as may be subsequently amended (the “Registration Statement”), filed with the Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended (the “Securities Act”), in connection with the sale by the Company of up to 11,500,000 shares (the “Shares”) of the Company’s common stock, par value $0.01 per share (“Common Stock”).

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

In connection with this opinion, we have examined originals or copies, certified or otherwise identified to our satisfaction, of (i) the Amended and Restated Certificate of Incorporation of the Company as in effect on the date hereof, (ii) the Amended and Restated Bylaws of the Company as in effect on the date hereof, as certified to us by a Company officer, (iii) the Amended and Restated Bylaws of the Company as in effect at the time of the adoption of the resolutions by the Board of Directors approving the issuance of the Shares, as certified to us by a Company officer, (iv) an underwriting agreement to be entered into by the Company and the underwriters (the “Underwriting Agreement”), (v) certain resolutions of the Board of Directors of the Company and the Pricing Committee of the Board of Directors of the Company, as certified to us by a Company officer, and (vi) such other documents and records as we have deemed necessary and relevant for purposes hereof. We have relied upon certificates of public officials and officers of the Company as to certain matters of fact relating to this opinion and have made such investigations of law as we have deemed necessary and relevant as a basis hereof. As to all matters of fact material to such opinion, we have relied upon representations of officers of the Company.

In our examination, we have assumed and have not independently established or verified (i) the genuineness of all signatures, (ii) the legal capacity of all natural persons, (iii) the authenticity of all documents submitted to us as originals, and (iv) the conformity to the authentic originals of all documents supplied to us as certified, conformed, photostatic or faxed copies.

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Based upon the foregoing, and subject to the limitations and assumptions set forth herein, and having due regard for such legal considerations as we deem relevant, we are of the opinion that when issued, sold and paid for in accordance with the Underwriting Agreement, the Shares will be validly issued, fully paid and non-assessable.

The foregoing opinion is based on and is limited to the General Corporation Law of the State of Delaware (which is deemed to include the statutory provisions thereof, applicable provisions of the Delaware Constitution and reported judicial opinions interpreting the foregoing), and we render no opinion with respect to the laws of any other jurisdiction.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. We also consent to the reference to our firm under the caption “Legal Matters” in the Registration Statement and the prospectus which forms a part thereof. In giving these consents, we do not hereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations issued thereunder.

This opinion is expressed as of the date hereof, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein, or of any subsequent changes in applicable law.

Respectfully submitted,

/s/ Andrews Kurth LLP