The role of teacher agency in professional learning has been the subject of several qualitative studies but has not yet been tested in an experimental setting. To provide causal evidence of the impact of teacher agency on the effectiveness of professional learning, we conducted a preregistered randomized controlled trial in an online computer science course with volunteer instructors who teach students worldwide. All instructors (N=583) received automated feedback on their instruction throughout the course, with half randomly assigned to have choice over the feedback topic. While choice over feedback topic alone did not significantly impact instructors' engagement with feedback or measured changes in their instruction, it led to improved student attendance--an effect that was strongest for instructors who actively engaged with additional professional learning resources, including training modules and teaching simulations. For this motivated subset of instructors, having choice over feedback had significant positive impacts on both their instruction and student outcomes compared to the control group. These findings suggest that agency in professional learning may be most effective when combined with instructors' intrinsic motivation to pursue self-directed improvement. Our study paves the way for further empirical investigations into when and how agency can be effectively integrated into professional learning systems.