Nonlinearities in lattices with topological band structures can induce topological interfaces in the bulk of structures and give rise to bulk solitons in the topological bandgaps. Here we study a photonic Chern insulator with saturable nonlinearity and show the existence of topological bulk solitons. The fundamental bulk solitons exhibit as semi-vortex solitons, where only one pseudospin component has a nonzero vorticity. The bulk solitons have equal angular momentum at different valleys. This phenomenon is a direct outcome of the topology of the linear host lattice and the angular momentum can be changed by switching the sign of the nonlinearity. The bulk solitons bifurcate from the linear bulk band edge and terminate when their powers saturate. We find that these bulk solitons are stable within the whole spectrum range. Moreover, these bulk solitons are robust against lattice disorders both from on-site energies and hopping amplitudes. Our work extends the study of Chern insulators into the nonlinear regime and highlights the interplay between topology and nonlinearity.