Is it possible to deploy Alexa skill using circleCI?
I haven’t done it, but the answer is likely to be yes. If you can do a scripted deployment from your dev machine, then you can do it from a CI system.
Could you research how to do this in general, by searching for “Deploy Alexa skill on Linux”? 
That will give you the information you need - the only difference will be how to handle secrets/passwords/tokens to authenticate you to the Alexa servers. You can use CircleCI environment variables for that.
Good luck! 