This sentence is not active (with or without "was"). The instructor does the assigning. The textbook is not the subject for the verb "assign," because no matter how you slice it, the logic here is "instructor assigns textbook" not "textbook assigns itself."
To truly make the sentence active voice:
Our instructor assigned a new textbook focused on recent advances in artificial intelligence.
To correct it, as is, you do need to add "was." That's not converting it to passive, it's simply correcting the passive-voice sentence that already exists.
Stangdon's comment made me realize there is another option for making this sentence into active voice. The following two sentence fragments have the same construction—a noun (textbook) modified by a past participle phrase:
Textbook focused on recent advances in artificial intelligence
Textbook assigned by our instructor
These are both grammatical, but neither has a main verb or is a complete sentence. You can choose which one you want to make into the main verb and which one you want to leave as the modifier, so the following sentence would be a valid active-voice sentence, too:
A new textbook assigned by our instructor focuses on recent advances in artificial intelligence.
The textbook is the thing doing the "focusing," so in this option "textbook" can be the subject.