As mentioned in [tfb's answer][1], the deflection in special relativity is half that of general relativity. In the special relativity treatment, the effect is Newtonian (a "gravitational force" interacting directly and instantaneously between two masses). Consider a single photon passing a body of mass <I>M</I> at a distance <I>r</I>. The Newtonian deflection angle is: $$\theta= \frac{2GM}{rc^2}$$

In general relativity, the deflection angle is: $$\theta= \frac{4GM}{rc^2}$$.
This is because, in effect, while special relativity considers the warpage of time, general relativity considers spacetime warpage.

One interesting feature to point out is that in the Newtonian approach, the passing object will experience an increase in speed (potential energy converted into kinetic energy). However, according to relativity, a photon cannot be accelerated past <I>c</I>. Instead, the transfer of this energy causes the photon's frequency to increase as it passes through a gravitational well (and decrease upon escaping); this is the phenomenon of gravitational redshift. The energy of a photon is given by $e=h\nu$, where <I>h</I> is Planck's constant, and $\nu$ is the frequency, thus it can be seen that energy and frequency are directly proportional to Planck's constant.

  [1]: https://physics.stackexchange.com/questions/425890/doesnt-special-relativity-predict-gravitational-bending-of-light/425891#425891