Ionospheric scintillation can cause BeiDou system (BDS) signal amplitude fading and phase variation as the radio frequency (RF) signals pass through the ionosphere. With the accidental, sudden, and regional characteristics of ionospheric scintillation, it is difficult to effectively mitigate the impacts of ionospheric scintillation from a system perspective. To overcome this problem, this work addresses the mitigation of scintillation for the BDS signal. We propose an adaptive wavelet denoising unscented Kalman filter (WDUKF)-based carrier tracking algorithm to mitigate the adverse impacts of ionospheric scintillation. First, as WD can better characterize the nonstationary of signal, the non-Gaussian noise caused by scintillation can be filtered by designing a sliding window-based online WD filter. Second, taking the denoised integrations as an input, we employ the phase lock indicator (PLI)-based adaptive UKF carrier phase estimator to reduce the linearization approximate error of conventional KF-based algorithms. Through adjusting the measurement vector of UKF with different scintillation scenarios adaptively, the divergence problem of UKF can be mitigated. Simulation and real data experimental results demonstrate the validity of the proposed method, especially in the case of 36 dB-Hz in moderate scintillation, the phase jitter and probability of loss-of-lock decrease about 6 deg (40%) and 71%, respectively.