In this paper, we define Clairaut semi-invariant Riemannian map ${F}$ from a Riemannian manifold $(M, g_{M})$ to a Kähler manifold $(N, g_{N}, P)$ with a non-trivial example. We find necessary and sufficient conditions for a curve on the base manifold of semi-invariant Riemannian map to be geodesic. Further, we obtain necessary and sufficient conditions for a semi-invariant Riemannian map to be Clairaut semi-invariant Riemannian map. Moreover, we find necessary and sufficient condition for Clairaut semi-invariant Riemannian map to be totally geodesic. In addition, we find necessary and sufficient condition for the distributions $\bar{D_1}$ and $\bar{D_2}$ of $(ker{F}_\ast)^\bot$ (which are arisen from the definition of Clairaut semi-invariant Riemannian map) to define totally geodesic foliation. Finally, we obtain necessary and sufficient conditions for $(ker{F}_\ast)^\bot$ and base manifold to be locally product manifold $\bar{D_1} \times \bar{D_2}$ and $N_{(range{F}_\ast)} \times N_{(range{F}_\ast)^\bot}$, respectively.