Electromagnetic properties of diquarks are investigated in the framework of a Nambu-Jona-Lasinio model, which describes baryons as bound states of diquarks and quarks. We calculate the electromagnetic form factors of scalar and axial vector diquark bound states using the gauge-invariant proper-time regularization. The nucleon charge radii and magnetic moments are estimated in a simple additive diquark-quark model. This picture reproduces the qualitative features such as the negative charge radius of the neutron. Within this model axial vector diquarks are seen to be important.