Yes, there are mobile casinos that offer a no deposit bonus to new players. You'll find many online casinos that offer no deposit bonuses to new players that access their casinos directly from a computer, but there are limits when it comes to players that want to use a mobile device.
Online casinos are still playing catch-up with the mobile industry, and not all of the online casinos with a no deposit bonus offer games on a mobile device. Those that do offer mobile games, only tend to offer their best titles for mobile players which limits the variety of games to play.
For the best mobile gaming experience with a no deposit bonus, look for the online casinos that cator only to mobile players. The online casinos that are solely focused on mobile gamers tend to offer a better variety of games, bonuses, and compatibility for mobile players.