  We present a method to compute non-perturbatively the renormalization
constant of the scalar density for Ginsparg-Wilson fermions. It relies on
chiral symmetry and is based on a matching of renormalization group invariant
masses at fixed pseudoscalar meson mass, making use of results previously
obtained by the ALPHA Collaboration for O(a)-improved Wilson fermions. Our
approach is quite general and enables the renormalization of scalar and
pseudoscalar densities in lattice regularizations that preserve chiral symmetry
and of fermion masses in any regularization. As an application we compute the
non-perturbative factor which relates the renormalization group invariant quark
condensate to its bare counterpart, obtained with overlap fermions at beta=5.85
in the quenched approximation.
