I'm not sure you can do this directly with PS. PS will use the fonts installed in the system or the fonts installed in C:\Program Files\Common Files\Adobe\Fonts (on Windows).
One way to do this would be create a shared folder on your network and synchronize this shared folder with the ...Adobe\Fonts folder.
I was able to get this to work using Dropbox as suggested by @plainclothes. To get a painless, cross-platform solution, you might need some assistance from your system admin.
Here's what I did on my PC. I don't have a Mac to try this on but a similar approach should work
- Create an account on Dropbox and install the dropbox application on your PC.
- Within your local Dropbox (typically c:\Users\username\Dropbox) directory create a directory to hold your fonts.
- Next open a command window on your PC in administrator mode (Start->type 'cmd'->right click on 'Run as Administrator')
- create a symlink to the Dropbox/Fonts folder using mklink
On my PC I did this with the command below
C:\Program Files\Common Files\Adobe> mklink /D Fonts C:\Users\Dinesh\Dropbox\Fonts
symbolic link created for Fonts <<===>> C:\Users\Dinesh\Dropbox\Fonts
I was in the Adobe directory when I created the link but it should work regardless of where you are as long as you are in admin mode.
With the symlink created I'm able to access the fonts in my Dropbox folder using Photoshop. And it syncs both ways i.e. I can drop a font file into my local folder at it shows up on dropbox. You'll need to share the font folder on dropbox with the rest of your team or create an account specifically for this purpose that everyone has access to.
Hope this helps.