We demonstrate atomic force microscopy (AFM) imaging with a microcantilever force transducer where an integrated superconducting microwave resonant circuit detects cantilever deflection using the principles of cavity optomechanics. We discuss the detector responsivity and added noise, pointing to its crucial role in the context of force sensitivity. Through analysis of noise measurements we determine the effective temperature of the cantilever eigenmode and we determine the region of detector operation in which the sensor is thermal-noise-limited. Our analysis shows that the force-sensor design is a significant improvement over piezoelectric force sensors commonly used in low-temperature AFM. We discuss the potential for further improvement of the sensor design to achieve optimal detection at the standard quantum limit. We demonstrate AFM operation with surface-tracking feedback in both amplitude-modulation and frequency-modulation modes.