A method is presented for the automatic construction of an experimental bifurcation diagram of an optically injected solid state laser. From measured time series of laser output intensity, different identifiers of aspects of the dynamics are derived. Combinations of these identifiers are then used to characterize different possible bifurcations. The resulting experimental bifurcation diagram in the plane of injection strength versus detuning includes saddle-node, Hopf, period-doubling and torus bifurcations. It is shown to agree well with a theoretical bifurcation analysis of a corresponding rate equation model.