Yes. Persian is an Iranian language within the Indo-Iranian branch of the Indo-European languages

They are Iranian languages within the Indo-Iranian branch of the Indo-European language family.

Louis H. Gray has written:

'Mythology of All Races'

'Indo-Iranian phonology with special reference to the middle and new Indo-Iranian languages' -- subject(s): Phonology, Indo-Iranian languages

'Subandhu's Vasavadatta'

The ancient Aryans are believed to have spoken a language known as Proto-Indo-Iranian, which later evolved into two distinct language branches: Indo-Aryan (Sanskrit, Hindi, Bengali, etc.) and Iranian (Persian, Kurdish, Pashto, etc.).

Persian Language, also known as Farsi, is the most widely spoken member of the Iranian branch of the Indo-Iranian languages