Yes, he signed it on June 4, 1963. The text of the Executive Order can be found online:
SECTION 1. Executive Order No. 10289 of September 19, 1951, as
amended, is hereby further amended --
(a) By adding at the end of paragraph 1 thereof the following
"(j) The authority vested in the President by paragraph (b) of section
43 of the Act of May 12, 1933, as amended (31 U.S.C. 821 (b)), to
issue silver certificates against any silver bullion, silver, or
standard silver dollars in the Treasury not then held for redemption
of any outstanding silver certificates, to prescribe the denominations
of such silver certificates, and to coin standard silver dollars and
subsidiary silver currency for their redemption," and
(b) By revoking subparagraphs (b) and (c) of paragraph 2 thereof.
SEC. 2. The amendment made by this Order shall not affect any act
done, or any right accruing or accrued or any suit or proceeding had
or commenced in any civil or criminal cause prior to the date of this
Order but all such liabilities shall continue and may be enforced as
if said amendments had not been made.
However, I don't see anything in the text that would strip the Federal reserve of any power to loan money. Specifically, it only delegated existing Presidential power to the Treasury Department.
Further, Kennedy was vocal in his desire to stop using silver as a monetary metal, with a plan to replace silver certificates with Federal Reserve notes. That would seem to be at odds with the claim that he was trying to put the Fed out of business.