According to TechCrunch, an unnamed Twitter user came across the video.twitter.com site: Visiting the page resulted in a page that prompts you to "request access to publish video content"--but only if you have a verified Twitter account. The rest of us are out of luck for now.
Video ads on Twitter
Twitter has been making a big push toward giving advertisers additional flexibility for getting their message across, and its video play would seem to be the next step in this process. Twitter has already added cards that let you stream audio via its mobile app, for example, and back in April of last year, it toyed with cards that promoted app downloads.
For now, it appears that the video feature will be geared toward brands and advertisers, so you won't be able to upload your cat videos just yet. If demand from everyday users is high enough, however, it isn't unreasonable to think that the rest of us will get these newfangled video tools eventually.