Phase noise reduces target sensitivity in radar and increases bit error rate in telecommunications systems. Optoelectronic oscillators are known for using optical fibre technology to realise the large delay required to attain superior phase noise performance compared to conventional microwave source technology. However, the long fibre is vulnerable to environmentally induced phase perturbations, while conventional phase shifters have insufficient range to compensate for the phase drift over the operational temperature range without the use of a temperature-controlled enclosure. Here we introduce a vector modulator controlled by a Stuart-Landau integrator, as a solution to non-efficient tuning for the phase shift. The concept is verified by simulation and experimentally demonstrated using an optoelectronic oscillator phase-locked to a system reference. Phase lock is maintained over four free spectral ranges equivalent to a tuning phase range of 1440° when the optoelectronic oscillator is cycled over a 10 °C to 85 °C temperature range. These demonstrations highlight the practical potential of our continuous tuning method.