Actually, no—this is a common misconception. Einstein won the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect," not for his theories of relativity.

The photoelectric effect work, published in 1905, was foundational to quantum theory and demonstrated that light can behave as discrete packets of energy (later called photons).

Relativity was considered too controversial and not sufficiently experimentally verified at the time for the Nobel Committee's tastes. Einstein never received a Nobel Prize specifically for either special or general relativity.
