You may be thinking of Plato, who, according to Diogenes Laertius and his sources, "learnt gymnastics under Ariston, the Argive wrestler. And from him he received the name of Plato on account of his robust figure, in place of his original name which was Aristocles, after his grandfather, as Alexander informs us in his Successions of Philosophers. But others affirm that he got the name Plato from the breadth of his style, or from the breadth of his forehead, as suggested by Neanthes. Others again affirm that he wrestled in the Isthmian Games – this is stated by Dicaearchus in his first book On Lives." (Πλατυς meaning flat, or broad, cf. platypus, flat-foot.)

There's a lot of scarce and contradictory information about Socrates, as you can see from Laertius's account. It's not impossible he was a wrestler in among being a sculpter, rhetorician, and soldier, but he wasn't particularly well known for it.