You can't use any form of correlation, parametric or not, unless your variables are AT LEAST at the ordinal level of measurement. Otherwise, the concept of a correlation makes no sense.

Spearman's rho is used to correlate two ordinal variables or continuous variables that don't meet parametric test assumptions. If your variables are truly categorical (i.e., you can't place them in a logical order or hierarchy to say one is MORE or GREATER than another, etc.), then you can't use rho.

If you're looking at measures of association among categorical variables, you're probably going to use a chi-square test of some sort.