  Polarized X-ray source is an important probe for many fields such as
fluorescence imaging, magnetic microscopy, and nuclear physics research.
All-optical inverse Compton scattering source (AOCS) based on laser wakefield
accelerator (LWFA) has drawn great attention in recent years due to its compact
scale and high performance, especially its potential to generate polarized
X-rays. Here, polarization-tunable X-rays are generated by a
plasma-mirror-based AOCS scheme. The linearly and circularly polarized AOCS
pulses are achieved with the mean photon energy of 60($\pm$5)/64($\pm$3) keV
and the single-shot photon yield of $\sim$1.1/1.3$\times10^7$. A Compton
polarimeter is designed to diagnose the photon polarization states,
demonstrating AOCS's polarization-tunable property, and indicating the average
polarization degree of the linearly polarized AOCS is 75($\pm$3)%.
