Yes. You can use weapon finesse when attacking with your finger as an unarmed strke and when using it to deliver a touch attack.
Unarmed Strikes (your finger) counts as light weapons and qualify for weapon finesse.
From the d20pfsrd page about unarmed strike (emphasis mine)
An unarmed strike is always considered a light weapon. Therefore, you
can use the Weapon Finesse feat to apply your Dexterity modifier
instead of your Strength modifier to attack rolls with an unarmed
strike. Unarmed strikes do not count as natural weapons (see Combat).
The damage from an unarmed strike is considered weapon damage for the
purposes of effects that give you a bonus on weapon damage rolls.
However, This does not directly extend to making touch attacks. Touch attacks count as 'armed' unarmed attacks. Since unarmed attacks are considered light weapons, they qualify for weapon finesse.
“Armed” Unarmed Attacks: Sometimes a character's or creature's unarmed
attack counts as an armed attack. A monk, a character with the
Improved Unarmed Strike feat, a spellcaster delivering a touch attack
spell, and a creature with natural physical weapons all count as being
armed (see natural attacks).