"Gotten on the horn" is a colloquial phrase used to indicate making a phone call or initiating a conversation via telephone. There are several synonyms that can be used interchangeably with this phrase, including "picked up the phone," "dialed in," "made a call," or "rang up." Additionally, one could use the phrase "reached out" to refer to a phone call or message exchange. The choice of synonym may vary based on the context and tone of the conversation, but all convey the same essential meaning of initiating contact via telephone.