Verse 38 is written as a conditional promise and verse 39 refers to it as "For this promise".
Acts 2:
36 “Therefore let all the house of Israel know assuredly that God has made this Jesus, whom you crucified, both Lord and Christ.”
37 Now when they heard
this, they were cut to the heart, and said to Peter and the rest of the apostles, “Men
and brethren, what shall we do?”
38 Then Peter said to them, “Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit. 39 For the promise is to you and to your children, and to all who are afar off, as many as the Lord our God will call.” 40 And with many other words he testified and exhorted them, saying, “Be saved from this perverse generation.”
41 Then those who gladly received his word were baptized; and that day about three thousand souls were added
to them.
Breaking down the conditional promise of Verse 38:
The Condition is:
Repent, and let every one of you be baptized in the name of Jesus Christ
The Promise for meeting the condition is:
for the remission of sins; and you shall receive the gift of the Holy Spirit.
Verse 39 is saying that the conditional promise in verse 38 is universal and goes on for many generations. Jesus (the Lord our God) commands the Body of Christ (His agency on the earth) to put forth the call to all men in the Great Commission. Talking about arbitrary - you seem to think that the condition to receive the promise is "
as many as the Lord our God will call". That's an odd rendering of the text.