Exhibit 23

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the following Registration Statements:

(1) Form S-8 (No. 333-195993), and

(2) Form S-3 (No. 333-183772);

of our reports dated February 26, 2015, with respect to the consolidated financial statements of American Capital Mortgage Investment Corp., and the effectiveness of internal control over financial reporting of American Capital Mortgage Investment Corp., included in this Annual Report (Form 10-K) of American Capital Mortgage Investment Corp. for the year ended December 31, 2014.

McLean, Virginia     /s/ Ernst & Young

February 26, 2015