Optical and electronic properties of black phosphorus strongly depend on the number of layers and type of stacking. Using first-principles calculations within the framework of density functional theory, we investigate the electronic properties of bilayer black phosphorus with an interlayer twist angle of 90°. These calculations are complemented with a simple k p model which is able to capture most of the low energy features and is valid for arbitrary twist angles. The electronic spectrum of 90° twisted bilayer black phosphorus is found to be x-y isotropic in contrast to the monolayer. However x-y anisotropy, and a partial return to monolayer-like behavior, particularly in the valence band, can be induced by an external out-of-plane electric field. Moreover, the preferred hole effective mass can be rotated by 90° simply by changing the direction of the applied electric field. In particular, a +0.4 (-0.4) V A-1 out-of-plane electric field results in a ~60% increase in the hole effective mass along the y (x) axis and enhances the my /mx (mx /my) ratio as much as by a factor of 40. Our DFT and k p simulations clearly indicate that the twist angle in combination with an appropriate gate voltage is a novel way to tune the electronic and optical properties of bilayer phosphorus and it gives us a new degree of freedom to engineer the properties of black phosphorus based devices. © 2017 IOP Publishing Ltd.