American Security Bank announced yesterday that it will join the first nationwide bank link of automated teller machines and said that by early 1983 American Security customers will be able to get cash from their accounts at teller machines from New York to Chicago to the West Coast.

The so-called Plus system will connect teller machines at 33 banks. Operators of the system, based in Colorado, hope that dozens of additional banks will join within the next few months.

Three of the nation's 10 biggest banks--Bank of America in California, Continental Illinois in Chicago and Chase Manhattan in New York--are charter members of the Plus system. Several large regional bank networks of automatic teller machines have been put in place during the last several years, but the Plus system is the first to join banks from coast to coast. A large regional network in the Rocky Mountains, headed by Denver National Bank, is the base on which the Plus system has been built.

American Security also is trying to develop a regional network of automatic teller machines and said its decision to become a charter owner of the Plus system does not affect its desire to form the regional operation.

Warren Minami, an American Security vice president who heads its electronic funds transfer division, said that an American Security customer in New York who needs money could go to a teller machine at Chase Manhattan, insert his or her card and get money from his or her American Security account "right on the spot."