Yes, it means a rumor. "The word" is the rumor. "Around" means that rumor, story, or information circulates. Everybody hears about it. "Gets," here, means "is achieved, somehow." It means "it happens, but I don't know how it happens." Here's another example of "the word" meaning information, news, or rumor: "The word is that Fred Wang is going to be promoted to head of the R&D department." Here is another example of "get" meaning "happens, somehow" or "is achieved, somehow:" "Something happened in his senior year and he got himself expelled from school."

Word gets around. = A rumor spreads (usually quickly).