Individual-level data sharing across multiple sites can be infeasible due to privacy and logistical concerns. This article proposes a general distributed methodology to fit Cox proportional hazards models without sharing individual-level data in multi-site studies. We make inferences on the log hazard ratios based on an approximated partial likelihood score function that uses only summary-level statistics. This approach can be applied to both stratified and unstratified models, accommodate both discrete and continuous exposure variables, and permit the adjustment of multiple covariates. In particular, the fitting of stratified Cox models can be carried out with only one file transfer of summary-level information. We derive the asymptotic properties of the proposed estimators and compare the proposed estimators with the maximum partial likelihood estimators using pooled individual-level data and meta-analysis methods through simulation studies. We apply the proposed method to a real-world data set to examine the effect of sleeve gastrectomy versus Roux-en-Y gastric bypass on the time to first postoperative readmission.