The legal way to do this is to introduce the blog in an offer and let them subscribe, assuming that they are opted in in the first place.
The CTA should be on the blog too.
Now it's possible that if you had a list with just a "general opt in" like
Opt In = T/F
and no other subscription choices, then those who opted in are expecting something from you. Whether it's your blog or another promo doesn't matter. Still, I prefer to invite them to your exclusive blog email list. Those who sign up will be more engaged.
Successful marketers have found that Subscription Management is far superiod. Give people several options for communications:
-Promos
-Webinars
-Events
-Blog
-etc
Never push your leads into content they haven't requested, otherwise their only choice is to Unsubscribe. Instead, subscription management offers choices and levels, so they rarely totally unsubscribe.