Aside from what was mentioned, you can also self-host perforce at a relatively low cost (provided you don't need more than 20 users, as that's all perforce's free license supports).

I personally host a perforce server on google compute engine for around $15 a month (g1-small + whatever size persistent disk you want). Relatively easy to set up (they provide repositories for ubuntu and fedora iirc), configuration is largely interactive when setting up or through the P4Admin tool (which allows you to very easily setup permissions, depots, etc).

I know that isn't fully managed like github and doesn't provide issue tracking, wikis, etc, but I've found it fairly easy to deal with if you know a bit of how to setup a linux VPS.

They are advertising for a while to offer a hosted service themselves: https://www.perforce.com/helix-ondemand

I did not try this though.

Assembla indeed offers hosted Perforce, (and hosted Git, and hosted Subversion, and even all three in the same workspace) but only as part of their collaboration suite. To get your money's worth, you'd also have to buy into their wiki and ticketing system (which does integrate into whatever repository you choose) and planning tools.

Which aren't bad, but may not be what you're looking for.