Exhibit 32.1

CERTIFICATION PURSUANT TO

SECTION 1350, CHAPTER 63 OF TITLE 18, UNITED STATES CODE,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to Section 1350, Chapter 63 of Title 18, United States Code, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, as Chief Executive Officer of Owl Rock Core Income Corp. (the “Company”), does hereby certify that to the undersigned’s knowledge:

1) the Company’s Form 10-K for the year ended December 31, 2021 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2) the information contained in the Company’s Form 10-K for the year ended December 31, 2021 fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: March 9, 2022	By:	/s/ Craig W. Packer
		Craig W. Packer
		Chief Executive Officer