You'll recall that imprecatory psalms are psalms that call down curses upon enemies and adversaries. The most famous one being Psalm 137, with its chilling line, "Happy is the one who seizes your infants and dashes them against the rocks."
Again, I'd assumed that Psalm 109 was also an imprecatory psalm. The psalm reads in the NIV:
1 My God, whom I praise,
do not remain silent,
2 for people who are wicked and deceitful
have opened their mouths against me;
they have spoken against me with lying tongues.
3 With words of hatred they surround me;
they attack me without cause.
4 In return for my friendship they accuse me,
but I am a man of prayer.
5 They repay me evil for good,
and hatred for my friendship.
6 Appoint someone evil to oppose my enemy;
let an accuser stand at his right hand.
7 When he is tried, let him be found guilty,
and may his prayers condemn him.
8 May his days be few;
may another take his place of leadership.
9 May his children be fatherless
and his wife a widow.
10 May his children be wandering beggars;
may they be driven from their ruined homes.
11 May a creditor seize all he has;
may strangers plunder the fruits of his labor.
12 May no one extend kindness to him
or take pity on his fatherless children.
13 May his descendants be cut off,
their names blotted out from the next generation.
14 May the iniquity of his fathers be remembered before the Lord;
may the sin of his mother never be blotted out.
15 May their sins always remain before the Lord,
that he may blot out their name from the earth...
The poem starts off as a prayer of supplication in verses 1-5. The poet calls out to God for help as the he is surrounded and being attacked by wicked people.
A shift comes with verse 6. Here the poet seems to begin to direct curses at his oppressors. And a long list of curses it is!
In short, the NIV assumes that the speaker in verse 6 is the poet who speaks curses against his enemies.
But there's actually some ambiguity about who, exactly, is speaking in verse 6. For example, here are verses 5 and 6 in the ESV:
5 So they reward me evil for good,
and hatred for my love.
6 Appoint a wicked man against him;
let an accuser stand at his right hand.
Where the NIV renders the line as "appoint someone to oppose my enemy," the more literal translation of the Hebrew in the ESV just has a pronoun: appoint someone against "him."
Well, "him" who? Obviously, the NIV thinks the "him" is "the enemy" described above in verses 1-5. And that's the way I've always read the psalm. But there's actually another way to interpret the "him."
Specifically, Robert Alter makes the argument that the speaker in verse 6 isn't the poet but the enemies of the poet. What starts in verse 6 are the enemies hurtling curses at the beleaguered poet. Here's Alter's translation of verses 5 and 6:
And they offer me evil in return for good
and hatred in return for my love:
"Appoint a wicked man over him,
let an accuser stand at his right hand..."
Alter's punctuation helps us see that the voice that starts to speak in verse 6 is the collective voice of the poet's enemies who begin to accuse and curse the poet, offering him hatred and evil. Alter supports this translation by saying,
[The opening formula of the psalm, "God of my praise, do not be silent,"] aligns this text with the psalms of supplication. What is unusual about this particular supplication is that the long central section of the psalm, verses 6-19, is, in the most persuasive reading, an extensive quotation of the venomous words of accusation and imprecation that the speaker's accusers pronounce against him.
[Starting in verse 6, the words "Appoint a wicked man over him"] inaugurate the hostile speech of the accusers. A clue to the fact that the speaker is the object of the curse is that the reviled man is referred to throughout in the singular, whereas the plural is for his accusers. Their speech includes both scathing curses against the man and his family and specific indications that they want to frame a case against him in a court of law.
All that to say, Psalm 109 does have a lot of imprecations in it, but it might not be an imprecatory psalm.