Technically, yes, but it's not a matter of using the general feat Bow Feint (Dragon #350 90) in isolation. To realize the feat's benefit, the creature "must have a ranged weapon readied (and loaded, if applicable)." Then, if the feint is successful, "the
next ranged attack [the creature] makes against that target does not allow [the target] to use his Dexterity bonus to AC."
In other words, if otherwise unarmed, an arcane trickster can't realize the benefit of the feat Bow Feint—the arcane trickster typically isn't already wielding a spell so can't use the feat. He could, though, if armed with, a loaded light crossbow, use the feat then cast a spell.
For example, an arcane trickster that's wielding a loaded light crossbow on turn 1 takes a standard action use the feat Bow Feint and succeeds. On turn 2, that arcane takes a free action to remove one hand from the light crossbow then takes a standard action to cast a spell that requires a ranged touch attack. The foe that the arcane trickster successfully feinted on turn 1 would be denied his Dexterity bonus to AC against the trickster's spell.
This is complicated, and usually not worth the trouble. The arcane trickster will usually be better off on turn 1 casting a spell that denies his foe his Dexterity bonus to AC, like grease or sleet storm (and, in this latter case, having a way to see through it), or casting a spell that just outright removes his foe from the battle.