I write articles on medium.com.
Medium.com allows us to embed a gist, GIF.
Is there any way to embed asciinema to Medium?
Did you check the docs? (presumably not 
)
https://asciinema.org/docs/embedding
See the point at the end of the page above, where it details using oEmbed (which is a method of sites exposing embeddable content for other sites to use). On the Medium side, details of oEmbed are here:
https://help.medium.com/hc/en-us/articles/214981378-Using-embeds (or Google it if you want some more hand-holding examples of how it works as a few people have written articles on it for a variety of oEmbed sources, but it’s pretty self explanatory)
Hey I just opened a post on this here Add support for embed.ly
It seems medium uses embed.ly for supporting 3rd party embeds. This is a paid service so I’m not sure what the maintainers think of adding this support.