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She has graduated [in / since] 1990.

This sentence is in my homework and I don't know which answer I should choose.

Choosing since doesn't make the sentence meaningful I think the correct answer is in even that my teacher says since

Neither you nor your teacher are correct, as neither "in" nor "since" would be grammatical.

The problem is with the present perfect has graduated, which is an awkward conjugation of the verb. There are few cases where it makes sense, as it indicates an action recently completed. For example:

He has recently graduated from college

He has graduated from college, but he's considering going back for a graduate degree

Some people might use it to talk about the school where you graduated from:

He has graduated from Harvard.

However, in this case I would simply use the simple past "graduated" -- which is also what I would use when talking about the time frame:

She graduated in 1990.

Graduating is a single event, that does not normally continue over time, so you would never use "since" -- except perhaps ironically

Our lazy son has been "graduating" since 2015. Maybe this year it'll actually become official.

It is quite possible that different educational establishments refer to graduation in slightly different ways. In those establishments (in England) that I know about the usual form would be :"she graduated in...".

Using the word "since", as in "I graduated since five years" is a common mistake made by non-native speakers of English when the correct form is "... five years ago..."