Not quite. Einstein received the 1921 Nobel Prize in Physics, 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.

Why not relativity? Relativity — especially general relativity — was still viewed as new and controversial by some in the physics establishment despite popular attention (the 1919 eclipse tests). The Nobel Committee favored awarding work that had clear experimental support and practical impact, and Einstein’s explanation of the photoelectric effect provided a decisive theoretical basis for quantized light and was experimentally testable and confirmed.
