Altermagnets are fully compensated antiferromagnets that lack the combined time-reversal and translation symmetry. We show that their symmetry allows for a switchable ferro-spinetic polarization – the spin analogue of erroelectricity – in a direction dictated by the lattice symmetry. We demonstrate this effect in its purest form in an interacting altermagnetic fermion model, in which a many-body chiral symmetry forbids any charge polarization. Our quantum Monte Carlo simulations reveal edge-localized, reversible spin accumulations fully consistent with this symmetry locking. Additionally, we identify Mn-based metal-organic frameworks as realistic hosts for the ferro-spinetic altermagnetic effect.