Acts 2:39

For to you is the promise, and to your children, and to all that are afar off, even as many as the Lord our God shall call unto him.

All that are afar off ... certainly includes the Gentiles; but Peter, like many of the prophets of the Old Testament, was here uttering words, under the power of his inspiration, that he himself did not fully understand; for it took a miracle, later on, to convince Peter that the Gentiles should be included as proper recipients of the gospel message. See under Acts 10:14,15, and also 1 Peter 1:12.

As a matter of simple fact, the command to believe, repent and be baptized for the forgiveness of sins (the Nestle Greek text translates this "with a view to" the remission of sins) and with the promise of receiving the Holy Spirit afterward, - this is a timeless and universal commandment of the Christian gospel, as clear from this verse. None are exempted, or denied, or promised redemption without compliance.