No – it wasn’t until the 22nd Amendment, passed in 1951, that Presidents were limited to only serving two-terms. Typically, Presidents would only serve two terms, because President George Washington set precedent by leaving office after two terms. However, nothing was legally stopping them to serving more than two terms (if they could get re-elected of course).
After Franklin Delano Roosevelt, who was elected for four terms, Congress decided that it was time to change that. The 1944 Republican nominee Thomas Dewey said, “Four terms… is the most dangerous threat to our freedom.”