In this work we demonstrate a tunable liquid–crystal element of linear phase profile along the radial coordinate. In combination with a regular refractive axicon, it behaves as an anisotropic axicon, generating the collinear superposition of two orthogonally polarized Bessel beams with different propagation constant. This superposition results in a Bessel beam where the state of polarization (SOP) varies periodically along propagation. Experimental results probe the voltage control of the SOP oscillating period, which agree well with theory. This compound axicon is a very compact and efficient way of generating Bessel beams with polarization modulation, thus representing a significant advantage over other methods reported in the literature that require bulk optical systems based on spatial light modulators.