Federal Computer Systems Protection Act of 1983 - Amends the Federal criminal code to establish penalties for using or attempting to use certain computers with intent to defraud, obtain property by false pretenses, embezzle, steal, or knowingly convert the property of another. Limits the kinds of computers covered by this Act to those operating in interstate commerce or operating on behalf of the Federal Government or a financial institution (where the prohibited conduct directly affects the computer operation).

Specifies factors which Federal law enforcement officers must consider in determining whether to exercise jurisdiction over such offense, where concurrent jurisdiction exists with a State or local government.

Directs the Attorney General to report annually to Congress on the extent of the exercise of such Federal jurisdiction.