The phrase 'gives a jingle' essentially means to give a call or make a phone call. There are various synonyms for this phrase that can be used interchangeably in different contexts. Some of the popular synonyms for 'gives a jingle' include 'calls', 'rings up', 'dials', 'phones', 'reaches out', 'contacts', and 'gets in touch with'. Each of these synonyms carries a slightly different connotation, and the choice depends on the context in which it is being used. For example, "I just wanted to give you a quick call" implies an informal conversation, while "I need to reach out to my boss about a deadline" indicates a more professional communication.