6tag is a pretty full featured Instagram app, but up till now it did not allow you to upload videos previously recorded on your phone.
The app will also feature new video filters in a later update.
While Windows Phone does have an official Instagram app, that app is still in beta and has not been updated in more than a year, lacking much of the new social networking features of the app which are on iOS and Android.
6tag is free and the current version can be found in the Windows Phone Store here.
Thanks SaeedZeroOne for the tip.