Learn French: Ci-joint le relevé annuel de votre compte. - Attached is the annual statement of your account.

No, it would remain Ci-joint la facture. When ci-joint (or ci-inclus) is placed at the very beginning of a sentence, it acts as an adverb meaning "herewith attached" and is entirely invariable. It only agrees with the noun if it is placed after it, where it acts as a regular adjective.

Where is the verb in this sentence?

There isn't one! In formal letters and emails, placing ci-joint at the very start of a sentence followed directly by a noun is a standard, polite shortcut. It acts as a stand-in for a full phrase like Veuillez trouver ci-joint... (Please find attached...).

Could I rewrite this to place ci-joint after the noun?

Yes, but you would usually need a full sentence with a verb. If you move it after the noun, it becomes a true adjective and must agree in gender and number. For example: Le relevé annuel de votre compte ci-joint a été envoyé (The attached annual statement of your account was sent).

What is the exact meaning of un relevé in this context?

In administrative and financial contexts, un relevé is a statement, transcript, or summary. It comes from the verb relever, which can mean to record or note down. Un relevé de compte is the standard French term for a bank statement.