Yes, indeed he did. He even wrote a piano concerto. I stole this online:
"Former President Nixon is known for many performances: his televised debate with John F. Kennedy, the Checkers speech, the Watergate hearing and his interviews with David Frost. But one of his most awesomely bizarre and at the same time humanizing performances is seen here, in an appearance on Jack Parr's Tonight Show. Nixon, who wrote this short piano concerto, tickles the ivories with full orchestral accompaniment — and even more astounding, manages to come off as relaxed, funny and even slightly charming."
Gosh how incredible, who’d have thought.