Can I create a Roblox game and play it on Xbox?

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YES!!  You can create Roblox games using Roblox Studio tools on a PC or Mac, and then play them on PC, Tablet, and Smart Phones and can now permit console access for your own game AND the whole Roblox Library.
 
Please check out this Blog Article for the most updated information on how to create your games and permit console access.  
 
If you think your game is ready to be highlighted on the “Featured” list, send an email to XboxSubmissions@Roblox.com with a link to the place for our consideration. For information on guidelines regarding featured games, please see the following Roblox Wiki page: Xbox Featuring Guidelines
 
Featured games will be displayed on the Xbox One home screen, which greatly increases click-through rates. Remember all games will be tested on Xbox and held to Microsoft Xbox requirement standards, so ensure your game and GUIs are gamepad ready!
 
To learn more about creating Roblox games check out the Roblox Wiki and if you want more information on implementing gamepad controls check out the Gamepad tutorial.