Technology based on high-peak-power lasers has the potential to provide compact and intense radiation sources for a wide range of innovative applications.In particular,electrons that are accelerated in the wakefield of an intense laser pulse oscillate around the propagation axis and emit X-rays.This betatron source,which essentially reproduces the principle of a synchrotron at the millimeter scale,provides bright radiation with femtosecond duration and high spatial coherence.However,despite its unique features,the usability of the betatron source has been constrained by its poor control and stability.In this article,we demonstrate the reliable production of X-ray beams with tunable polarization.Using ionization-induced injection in a gas mixture,the orbits of the relativistic electrons emitting the radiation are reproducible and controlled.We observe that both the signal and beam profile fluctuations are significantly reduced and that the beam pointing varies by less than a tenth of the beam divergence.The polarization ratio reaches 80％,and the polarization axis can easily be rotated.We anticipate a broad impact of the source,as its unprecedented performance opens the way for new applications.