A pump is disclosed. The pump may have a housing, a body rotatably disposed within the housing and at least partially defining a plurality of barrels, a plurality of plungers associated with the plurality of barrels, and a swashplate tiltable by a swivel torque to vary a displacement of the plurality of plungers relative to the plurality of barrels. The pump may also have a port plate with an inlet port, a discharge port, and a protrusion. The port plate may be configured to engage an end of the rotatable body. The pump may further have at least one piston disposed within the housing and configured to selectively engage the protrusion of the port plate to rotate the port plate and adjust the swivel torque.