When you have a soul gem containing a soul in your inventory, simply go to your Items menu, select Weapons, then scroll to the weapon you wish to recharge. However, in Skyrim, recharging is much simpler.
In other words, Soul Trap-enchanted weapons will let followers trap souls, but the followers won’t use those soul gems to recharge. Now, followers can make it way easier to fill soul gems (unless this has been patched) by filling an entire stack when they capture a soul, but they won’t recharge depleted weapons.
Just be sure to keep the weapon you’ve given them recharged. Yes they can! This is an easy way to take some of the hassle and headache out of the whole soul-management process.
