"Give a jingle" is a colloquial phrase which means to make a quick phone call or to contact someone through a phone call. There are various other synonyms to this phrase such as call up, phone, ring up, give a buzz, give a bell, give a tinkle, make a call, and dial up. All of these synonyms refer to the act of communicating with someone through the use of a telephone. Depending on the context and the tone of the conversation, these synonyms can be used interchangeably to convey the message of reaching out to someone through a phone call.