Moving pacman is not the right approach.
You do, however, have a couple of options. All of them assume that you already have a full and tested backup of your data.
First, make sure that you have cleared all available space in pacman's cache with
pacman -Sc: pass the second
c for everything. There is a pacman tool for more fine-grained control fo this, see
paccache --help for details.
If that still does not provide enough room, then you can resize your partitions with
fdisk which is part of
util-linux and is installed in the base group. There are a number of guides online for doing this.
The optimal solution, though, would be to grasp the nettle and do a full reinstall using LVM so that you have the flexibility to work around this issue (as well as other benefits like snapshotting) in the future. You could also fully encrypt your drive(s) while you are at it with LVM on LUKS.