If you have the patience to read his Wikipedia page (it's mostly about physics, so I haven't had the patience yet), it probably tells you all you need to know, but I know people for whom Wiki is never their main source.
I thought I'd summarise what I've found out. There are recordings (on Youtube) purporting to be of Einstein playing the violin, but they are all fake. They tend to be either Grumiaux or Flesch playing something simple - i.e. credible: if it had been Paganini, no-one would have been fooled. One was first uploaded specifically on April 1st and then re-uploaded by someone else a few months later.
And there was a musicologist called Alfred Einstein, a very distant relation, who confuses the picture for some.
However, Albert was forced by his mother to learn from the age of 5, and, although he quit (or did he rather play unwillingly?), he took it up again for pleasure in his early teens, so he was probably competent. The Juilliard Quartet appraised him as such 50 years later in somewhat mealy-mouthed language. In photos he seems relaxed, his left wrist is nice and straight. He seems to play a lot sul tasto, but then so did David Oistrakh, so maybe it was the style back then. Could it be something to do with gut?
To some extent his physics has resulted in much mythology, so we can probably expect mythology about his music. For example, if he and I played identically, he, due to his fame, would be appraised more highly than I would.
By mythology in physics, I mean things like, "he was a patents clerk when he invented General Relativity". No, he was a patents clerk while he studied physics at night school (or was it postally?). By the time he invented GR, he had been a professor at a university for years and was a year away from becoming the head of the German Physics institute (and not thanks to GR - it was years before people realised its importance)
Here's an attempt to trace Einstein's musical footsteps:
The article mentions him regularly playing Mozart and Beethoven sonatas. Supposedly his second wife Elsa fell in love with him after hearing him play Mozart, and a school examiner was very complimentary of his playing of a Beethoven sonata when he was 17. The consensus seems to be that he would not be mistaken for a professional, but was a very competent amateur.