You can apply infusions to the weapons of your Arcane Armor after you obtain that feature.
For reference, the relevant excerpts, emphasis mine.
Each of the armor’s gauntlets counts as a simple melee weapon while you aren’t holding anything in it, and it deals 1d8 thunder damage on a hit. A creature hit by the gauntlet has disadvantage on attack rolls against targets other than you until the start of your next turn, as the armor magically emits a distracting pulse when the creature attacks someone else.
A gemlike node appears on one of your armored fists or on the chest (your choice). It counts as a simple ranged weapon, with a normal range of 90 feet and a long range of 300 feet, and it deals 1d6 lightning damage on a hit. Once on each of your turns when you hit a creature with it, you can deal an extra 1d6 lightning damage to that target.
Both of these weapons count as simple, and are therefore valid targets for the Enhanced Weapon infusion.
Item: A simple or martial weapon
This magic weapon grants a +1 bonus to attack and damage rolls made with it.
Since your arcane armor is a single item until level 9, when you obtain Armor Modifications, it would take up the infusion slot for your arcane armor, but it is certainly a valid target for it.