Freely propagating electrons may serve as quantum probes that can become coherently correlated with other quantum systems, offering access to advanced metrological resources. We propose a setup that coherently couples free electrons in an electron microscope to a trapped-ion quantum processor, enabling non-destructive, quantum-coherent detection and the accumulation of information across multiple electrons. Our analysis shows that single electrons can induce resolvable qubit excitations, establishing a platform for practical applications such as quantum-enhanced, dose-efficient electron microscopy.