Actually, no. Einstein won the Nobel Prize in Physics in 1921, but it was awarded "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect" — not for relativity.

This is somewhat surprising given how transformative relativity was. At the time, relativity was still considered controversial by some, while the photoelectric effect was more universally accepted. The prize was awarded after he'd already developed both special and general relativity, so the choice reflects the Nobel committee's priorities of that moment rather than a ranking of his contributions.
