The originally classic Mega Man games will be seeing release on the App Store and Android Google Play storefront in January 2017. You can see the games in action on mobile with the above trailer. They look well enough but it seem that the frame rate has some stuttering or might not run at a locked frame rate. For a game like Mega Man, that might be a major issue considering how you need precise movement at all times.
But if you only have a mobile device and want to experience the series for the first time, you can play this in early 2017. However, if you own a portable system like the Nintendo 3DS, you can play the Legacy Collection to play the original three games with physical controls. The first four games in the Mega Man series (in addition to other games like Mega Man X4 and the Legends series) on the PS Vita through PS1 Classics support as well.