One of the existing prototype detector systems for full-field photon-counting CT is a silicon detector developed by our group. Spatial resolution is clinically important to resolve small details and can enable more efficient phase-contrast imaging. However, improving the resolution is difficult as decreasing the pixel size is associated with technical challenges. By integrating CMOS electronics into the silicon sensor, it is possible to reduce the pixel size drastically while also introducing on-sensor data processing capabilities. In this work, we evaluate the feasibility of measuring the charge cloud shape of Compton interactions in a silicon strip detector to increase the spatial resolution. With an incident spectrum of 140 kVp, Compton interactions constitute 66.2% of the detected interactions. By combining a Monte Carlo photon simulation with a charge transport model, we study the charge cloud distributions and induced currents as functions of the interaction position. For a simulated silicon strip detector with a pixel size of 12x500 mu m(2), we present a method in which the interaction position can be determined. For an ideal case without electronic noise an average absolute error of 0.65 mu m is obtained in the direction along the wafer and 13.08 mu m in the trans-wafer direction. With simulated electronic noise and a lowest threshold of 0.88 keV the corresponding values are 1.38 mu m and 122.83 mu m. Our results show that the proposed method has the potential to very significantly increase the spatial resolution in a full-field photon-counting detector for CT.