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There is no such built-in functionality. You would need a special database of all cities in US (if you want US only) or in the whole world that would tell you in which time zone a city lies. One US state may use multiple time zones, so you need a database at city (or, possibly, at least county level).
I have no idea if anybody provides such a database, but Oracle certainly does not. Note also that such database would change over time as time zone assignments change from time to time.