This thread is in the relativity section, and according to GR, "light" does produce gravity.
If you looked at a completely "empty" Universe that was void of any form of energy, matter, radiation, etc., in a 4 dimensional spacetime where
\mathbf{R(X,Y)Z}=R^{a}_{\ bcd}X^{c}Y^{d}Z^{b}=0=R_{bd}...