Learn Hardcore Croatian: Imam maramicu u torbici.

Because it’s the direct object of the verb imati (to have), and direct objects are typically in the accusative case.
Maramica is feminine singular, and many feminine nouns ending in -a change to -u in the accusative:

maramica (nominative) → maramicu (accusative)

Why is torbica written as torbici?

Because after u meaning in (location, not movement), Croatian uses the locative case.
Torbica is feminine singular, and the locative often ends in -i for this noun type:

torbica (nominative) → torbici (locative)

How do I know when u takes locative and when it takes accusative?

A common rule:

u + locative = location (being somewhere): u torbici = in the purse
u + accusative = movement into (going/putting into): u torbicu = into the purse

So compare:

Imam maramicu u torbici. = It’s already in there.