Catalyzes the formation of archaetidylinositol phosphate (AIP) from CDP-archaeol (CDP-ArOH or CDP-2,3-bis-(O-phytanyl)-sn-glycerol) and 1L-myo-inositol 1-phosphate (IP or 1D-myo-inositol 3-phosphate). AIP is a precursor of archaetidyl-myo-inositol (AI), an ether-type inositol phospholipid ubiquitously distributed in archaea membranes and essential for glycolipid biosynthesis in archaea. 1D-myo-inositol 3-phosphate + CDP-2,3-bis-O-(phytanyl)-sn-glycerol = CMP + H(+) + saturated 1-archaetidyl-1D-myo-inositol 3-phosphate Binds 2 Mg(2+) or Mn(2+) ions per subunit. Lipid metabolism; phospholipid metabolism. Belongs to the CDP-alcohol phosphatidyltransferase class-I family.