A micromechanical capacitive acceleration sensor is described for picking up the acceleration of an object in at least one direction. The sensor includes a frame structure (110), a sensor inertia mass (101) made of a wafer and movably mounted relative to the frame structure (110) about a rotation axis, and a capacitive pick-up unit (120) for producing at least one capacitive output signal representing the position of the sensor mass (101) relative to the frame structure (110). The sensor inertia mass (101) has a center of gravity which offset relative to the rotation axis in a direction perpendicularly to a wafer plane for measuring accelerations laterally to the wafer plane. The sensor mass (101) and the frame structure (110) are made monolithically of one single crystal silicon wafer. A cover section (112) forms a common connector plane (150) for the connection of capacitor electrodes (125,126). Torqueable elements (105) form an electrically conducting bearing device for the sensor mass (101).