AFAIK it's not enough to write it in your privacy policy. Art 21 of the GDPR makes this explicit:
> (4) At the latest at the time of the first communication with the data subject, the right referred to in paragraphs 1 and 2 shall be explicitly brought to the attention of the data subject and shall be presented clearly and separately from any other information.
I am not a lawyer, but as far as I can tell, there is no legal way to collect PII (including IP address) or place tracking identifiers on the user's device without at least informing the user explicitly under the GDPR and the ePrivacy Directive.