The surface rotational and translational displacement fields resulting from an arbitrarily oriented kinematic shear dislocation point source embedded in a horizontally stratified, semi‐infinite elastic medium are formulated in this article. The proposed formulation is based on the wavenumber integration method and is both concise and numerically stable. In the absence of recorded rotational ground motions, this formulation may be used to artificially generate those for a given site during an event, provided (a) the layered velocity model at the site and (b) the kinematic source parameters of the event are available. The proposed formulation is validated as well as suitable numerical examples are provided to illustrate how the formulation can be used to synthesize the rotational and translational ground motions in the case of a point source. It is possible to use the proposed formulation to synthesize these motions in the case of a finite fault as well.