The iPhone genuinely has no direct CSV import, and the clean answer routes through iCloud or another synced account, converting CSV to vCard along the way since that is what Apple's contacts accept. The reliable path:

The iCloud route, landing contacts on the phone through sync: the iPhone syncs contacts from iCloud, so getting the CSV into iCloud contacts puts them on the phone. iCloud contacts import vCard, not CSV, so the CSV converts to vCard first and Google Contacts is the free translator, import the CSV at contacts.google.com, export as vCard, then at icloud.com open Contacts and Import vCard, feeding that file. The contacts land in iCloud and sync to the iPhone within minutes, the same translator hop this forum uses for several contact tasks.

The alternative synced account route: if your iPhone syncs a Google or Outlook account for contacts rather than iCloud, import the CSV into that account instead, Google Contacts takes CSV directly and Outlook.com takes CSV through its People import, and the phone syncs those contacts down through the account it already uses, no vCard step needed since you import to the account in its native format.

The choice by what the phone already syncs: check Settings, Contacts, Accounts on the iPhone to see which accounts sync contacts, then import to whichever is there, iCloud via the vCard hop or a Google or Outlook account directly, since importing to an account the phone does not sync leaves the contacts stranded off the phone, the common mistake.

The verification: after importing to the right account, the contacts appear in the iPhone's Contacts app within a short sync, and a quick check of a few for correct names and numbers confirms the field mapping held through the conversion, since a CSV to vCard translation is where field mapping can slip, worth the glance for an important contact list.