You are true.
Have you watched a surfer or stood too close to the speakers at a rap concert which can tell you that waves carry momentum. Recall that the most general formulation of Newton's second law is not F=ma, but F=dp/dt, force equals the change of momentum with time. If there is a force, there is a transfer of momentum. Since electric and magnetic fields transmit forces, they transfer momentum. When two charged particles interact, momentum is transferred from one to the other via the electric and magnetic fields. We don't usually think of those fields as "carrying" the momentum from one to the other, since we treat the force as instantaneous; however, that is a perfectly valid way of looking at it. In fact, since force cannot be transferred faster than the speed of light, an exact treatment of such an interaction _has_ to take into account the time delay while the fields "carry" the force/momentum from one particle to the other. EM waves are essentially just self-sustaining, travelling fields.
Hope this helps.