In Acts 1:12-26 Peter says that Judas Iscariot had to be replaced (see Acts 1:16, 21). The vacancy his defection (and suicide) created could not be left open, otherwise Scripture would be broken. After all, what Judas had done and what, then, the remaining apostles had to do was prophesied, according to Peter, by David in the psalms, specifically in Pss 69:25 and 109:8 (see Acts 1:20). The problem with all this, however, is that on a first reading, at least, neither of these psalms is obviously prophetic, much less “spoke[n] . . . concerning Judas” (see Acts 1:16), which raises the question: Why did Peter think—and his hearers agree!—that these psalms warranted his claims and, therefore, called the early Christians to action?
The solution to this puzzle lies along the following two lines: (1) The early Christians read Pss 69, 109 and other psalms of lament messianically. They did this principally, I suspect, because this is the way Jesus read these psalms (see, e.g., John 13:18 [Ps 41:9], John 15:25 [Ps 35:19; 69:4]; John 19:24 [Ps 22:18]). Alongside of this, the early Christians elsewhere applied to Jesus’ resurrection/exaltation psalms originally describing David’s enthronement (see, e.g., Ps 2:7 in Acts 13:33; Heb 1:5; and Heb 5:5), suggesting they thought of Jesus as the greater and, indeed, true Davidic king. The psalms of lament were then likely drawn into this davidic ideology, this davidic typology, precisely because so many were already linked with David (i.e., “a psalm of David”) and, as well, because so many contained “forward-looking” elements—eschatological elements. (These forward-looking elements, moreover, probably explain the smattering of evidence suggesting that some of the laments were already read eschatologically—if not messianically—in the pre-Christian era. See, e.g., the interpretation of Ps 22 in 4Q88 or Ps 37 in 4QpPs37.) (2) If the early Christians read these laments typologically—that is, as prophesying about another, ultimate sufferer—then it’s not at all unlikely that they treated the enemies described in these psalms in a similar fashion. This indeed may explain why Peter changes “their place” in Ps 69:25 to “his place” (and, thus, “their tents” to “it”) in Acts 1:20a. Peter saw in the psalm’s description of betrayal the actions of the messiah’s ultimate betrayer, Judas Iscariot.
In short, Peter and the early Christians read Pss 69 and 109 messianically and, therefore, saw in them a description of Judas’ betrayal and a description of what should be done about his vacant post.