Can a pronoun placed before a noun show ownership?

Yes, that kind of pronoun is called a possessive adjective.

A possessive adjective is placed before a noun to describe that noun as belonging to someone or something.

The possessive adjectives are: my, your, his, her, its, our, their.

Examples:

My mother can pick us up.

What time is your appointment?

The dog was wagging its tail.

Several students raised their hands.