Yes, it does, or to be more precise, Newtonian gravitation predicts photons will be deflected if you assume photons have some mass.  However the amount of this deflection is just half of what GR predicts.  And the observed amount of deflection is what GR predicts (within experimental error).

There is a discussion of this in the [Wikipedia article on tests of GR](https://en.wikipedia.org/wiki/Tests_of_general_relativity#Deflection_of_light_by_the_Sun), and the [paper by Clifford M. Will](https://arxiv.org/abs/gr-qc/0510072) has more detail I think (disclaimer: I have not checked the latter in detail: it looks like section 3.4 & specifically 3.4.1 may be what you want).