There is no way to install custom distribution on DigitalOcean Droplet and Arch Linux is not one offered.
I will list you available distros on DigitalOcean and their versions.
||12.04, 14.04, 16.04, 16.10*
||11.0 zfs, 11.0, 10.3 zfs, 10.3, 10.2, 10.1
||1214.0.0 (alpha), 1185.2.0 (beta), 1122.3.0 (stable)
||7.2 (only x64), 6.8, 5.11
* Not a LTS (Long-Term Support) release, supported only until July 2017
** Available in both 64-bit and 32-bit versions (others are available only as 64-bit)
Beside that, there are One-Click Apps, which will install needed app for you. They’re usually based on Ubuntu 14.04/16.04.
You can suggest Arch Linux distro as idea on DigitalOcean UserVoice page.