Long-term quantum key distribution (QKD) using polarization encoding requires a random drift compensation method. We propose a method to compensate any state of polarization based on the quantum bit error rate (QBER) of two states from two non-orthogonal mutually unbiased bases. The proposed method does not require dedicated equipment, and through a simple but highly efficient feedback loop it compensates the polarization random drift suffered by photons while transmitted over the optical fiber quantum channel. A QBER lower than 2% was observed even considering imperfect single photon detectors. Besides, we verify a 82% secret key rate generation improvement in a finite-key size BB84 implementation for a 40 km fiber-optics quantum channel.