It is not inappropriate (I have one or two) - but you do have to make some considerations:
While it should be stated that you need to be careful with how you present yourself on social media, this gets more of an issue when you start adding workmates. Your new workmate friend may also be friends with another workmate who is friends with another colleague that you just bitched about - prepare for a frosty reception the next day. Or there's another chain to your boss and you've boasted about being hungover and calling in sick.
Would you regularly socialise with them outside of work? This is usually my benchmark, and I generally don't add a workmate until he is already an outside-of-work mate. This is more of a preference.
As Joe mentioned in his comment - some people are more guarded about who they add on social media, so don't read too much into it when someone rejects or doesn't respond to a friend request.