We report on a statistical analysis of the occurrence and properties of Alfvén ion cyclotron (AIC) waves in sheath regions driven by interplanetary coronal mass ejections (ICMEs). We have developed an automated algorithm to identify AIC wave events from magnetic field data and apply it to investigate 91 ICME sheath regions recorded by the Wind spacecraft. Our analysis focuses on waves generated by the ion cyclotron instability. AIC waves are observed to be frequent structures in ICME-driven sheaths, and their occurrence is the highest in the vicinity of the shock. Together with previous studies, our results imply that the shock compression has a crucial role in generating wave activity in ICME sheaths. AIC waves tend to have their frequency below the ion cyclotron frequency, and, in general, occur in plasma that is stable with respect to the ion cyclotron instability and has lower ion β‖ than mirror modes. The results suggest that the ion beta anisotropy β⊥/β‖>1 appearing in ICME sheaths is regulated by both ion cyclotron and mirror instabilities.