  We construct a geometric crystal for the affine Lie algebra D^{(1)}_n in the
sense of Berenstein and Kazhdan. Based on a matrix realization including a
spectral parameter, we prove uniqueness and explicit form of the tropical R,
the birational map that intertwines products of the geometric crystals. The
tropical R commutes with geometric Kashiwara operators and satisfies the
Yang-Baxter equation. It is subtraction-free and yields a piecewise linear
formula of the combinatorial R for crystals upon ultradiscretization.
