Hi DeaThere is a plugin that can help you do that if you are WordPress self hosted.There is some useful info here http://wordpress.org/support/topic/plugin-constant-contact-for-wordpress-importing-lacks-support-for-multiple-columns-in-csv

If you are aware of what you need to do the plugin should be able to import the email addresses with ease.

HTH

@deairby If your Constant Contant email list are opted-in to a newsletter, you could send them regular newsletters, maybe weekly summarizing your latest posts.  That could draw them to your blog.