We investigate the roughening of shear cracks running along the interface between a thin film and a rigid substrate. We demonstrate that short-range correlated fluctuations of the interface strength lead to self-affine roughening of the crack front as the driving force (the applied shear stress/stress intensity factor) increases towards a critical value. We investigate the disorder-induced perturbations of the crack displacement field and crack energy, and use the results to determine the crack pinning force and to assess the shape of the critical crack. The analytical arguments are validated by comparison with simulations of interface cracking.