We present arguments, based on local gauge invariance, that the multicritical point of Ising spin-glasses should be located on a particular line of the phase diagram known as Nishimori's line [tanh(βJ)=2p−1 for the ±J distribution]. One scaling axis is along the line, and the other is along the temperature direction. This scenario is generic for any random Ising model with a Nishimori line, in any number of dimensions, if the transitions are second order. The renormalization-group fixed point located inside Nishimori's manifold is expected to control multicriticality for a wider class of models.