I know this has been asked before, but most of them are 3 to 4 years ago with no definite answers. I would like to know if this is already possible as of 2015.
Yes, there is an API for an android VpnService (https://developer.android.com/reference/android/net/VpnService.html) which was added in API 14.
In addition, some CyanogenMod ROMs have an openvpn binary preinstalled.