  The Einstein's equivalence principle can be tested by using parameterized
post-Newtonian parameters, of which the parameter $\gamma$ has been constrained
by comparing the arrival times of photons with different energies. It has been
constrained by a variety of astronomical transient events, such as gamma-ray
bursts (GRBs), fast radio bursts as well as pulses of pulsars, with the most
stringent constraint of $\Delta \gamma \lesssim 10^{-15}$. In this letter, we
consider the arrival times of lights with different circular polarization. For
a linearly polarized light, it is the combination of two circularly polarized
lights. If the arrival time difference between the two circularly polarized
lights is too large, their combination may lose the linear polarization. We
constrain the value of $\Delta \gamma_{\rm p} < 1.6 \times 10^{-27}$ by the
measurement of the polarization of GRB 110721A, which is the most stringent
constraint ever achieved.
