וַאֲנִי נָסַ֣כְתִּי מַלְכִּ֑י עַל־צִיֹּון הַר־קָדְשִׁי
The verb נָסַכְתִּי appears to be the root נסך in the Qal binyan, which leaves rather slim pickings regarding translation. According to HALOT, the Qal means "to pour out." Pouring out to cast a statue is connoted in Isaiah 40:19. Is the psalmist here referencing the production of a statue of God? The KJV translates the verb "set."
Other possibilities have been suggested, though. If the verb is a Niphal, and the vocalization and assimilation of the nun has just been neglected, the verb can be translated "to consecrate," or "anoint." Another meaning in the Niphal is applicable, which would render the translation "woven," or "shaped."
We're thus left with the following possibilities for translation. Let me know which you prefer:
But I have consecrated/anointed/cast/formed my King upon Zion, his holy mountain.