  We investigate the circular photogalvanic effect (CPGE) in single-crystalline
methylammonium lead iodide microcrystals under a static electric field. The
external electric field can enhance the magnitude of the helicity dependent
photocurrent (HDPC) by two orders of magnitude and flip its sign, which we
attribute to magnetic shift currents induced by the Rashba-Edelstein effect.
This HDPC induced by the static electric field may be viewed as an unusually
strong third-order photoresponse, which produces a current two orders of
magnitude larger than second-order injection current. Furthermore, the HDPC is
highly nonlocal and can be created by photoexcitation out of the device
channel, indicating a spin diffusion length up to 50 $\mu$m at 78 K.
