  By using dimensionless conductances as scaling variables, the conventional
one-parameter scaling theory of localization fails for non-reciprocal
non-Hermitian systems such as the Hanato-Nelson model. Here, we propose a
one-parameter scaling function using the participation ratio as the scaling
variable. Employing a highly accurate numerical procedure based on exact
diagonalization, we demonstrate that this one-parameter scaling function can
describe Anderson localization transitions of non-reciprocal non-Hermitian
systems in one and two dimensions of symmetry classes AI and A. The critical
exponents of correlation lengths depend on symmetries and dimensionality only,
a typical feature of universality. Moreover, we derive a complex-gap equation
based on the self-consistent Born approximation that can determine the disorder
at which the point gap closes. The obtained disorders match perfectly the
critical disorders of Anderson localization transitions from the one-parameter
scaling function. Finally, we show that the one-parameter scaling function is
also valid for Anderson localization transitions in reciprocal non-Hermitian
systems such as two-dimensional class AII$^\dagger$ and can, thus, serve as a
unified scaling function for disordered non-Hermitian systems.
