Passengers will not be able to use cash to buy any items, including headsets, snacks, light meals and alcoholic drinks.
The airline said that it hopes to determine whether cabin passengers prefer to pay for their purchases with plastic or like to have the option to use cash.
Lauri Curtis, American Airlines' vice-president of onboard service, said: "These days, consumers are more frequently paying for items electronically with credit cards and debit cards.
"With this test, we are seeking feedback from passengers and from our flight attendants to determine if this consumer behaviour also works with the purchase of onboard items."
Ms Curtis explained that San Francisco was chosen for the test as departures from there cover an "excellent cross-section of distances", with flights going to Los Angeles, Dallas, Honolulu and New York among other destinations.
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(Tony Hill and Helen Gillilan)
