The radio frequency (RF) fingerprint technique is a robust method for security enhancement of the physical layer by leveraging the unique RF imperfections inherent in various wireless devices. Among these imperfections, the carrier frequency offset (CFO) stands out as a primary RF fingerprint (RFF) of the transmitter, offering the potential to distinguish among different transmitters. However, accurately estimating CFO in time-varying channels poses significant challenges due to multipath effects and Doppler shifts. In this paper, we focus on estimating CFO for wireless device identification in the orthogonal frequency division multiplexing (OFDM) communication system. To achieve precise CFO estimation under time-varying channels, we propose a frequency domain correlation and spline interpolation (FCSI) algorithm. This approach utilizes pilots distributed across different subcarriers to correlate with prior local sequences, facilitating accurate CFO estimation. Classification is then performed based on the Euclidean distance between the prior RFF and the tested RFF dataset. Simulation results demonstrate that the proposed M-consecutive average method effectively reduces the classification error rate in the challenging high-frequency (HF) skywave channel environment.