No—Einstein did **not** receive the Nobel Prize for relativity.

He was awarded the **1921 Nobel Prize in Physics** “for his services to Theoretical Physics, and especially for his discovery of the law of the *photoelectric effect*.”

Relativity (both special and general) was still controversial and not universally accepted by all members of the Nobel committee at the time, so they chose the photoelectric effect, which was experimentally well confirmed and seen as safer.
