Low Earth orbit (LEO) satellite communication (SATCOM) is a pivotal component of sixth-generation (6G) wireless communication. The dependability of satellite-to-ground communication is severely hampered by large-scale Doppler frequency offsets. We propose a carrier frequency offset (CFO) estimator applied to orthogonal time frequency space (OTFS) modulation. By inserting the pilot and maximum length sequences (MLS) for each OTFS frame in the delay-Doppler domain, the estimator can search for the corresponding equal-amplitude sequences and MLS along different dimensions in the delay-time domain. The fractional CFO, obtained by weighting the signal phase determined by the received sample’s correlation function, is the best linear unbiased estimate. The proposed estimator well enhances the estimation range by employing a correlation technique with MLS to estimate the large-scale CFO. Finally, we conduct numerous simulations on the time-varying channel. The results demonstrate a minimum of 53% reduction in frequency estimation error and a minimum 32-fold increase in estimation range compared with existing algorithms.