This is probably one of the less obvious things on Google+ but you can share your circles with someone else by going to G+ settings, data liberation and exporting your contacts. The screenshot below demonstrates the available options under Google+’s Data Liberation tab.

Download the zip file and open it, you’ll have all of your circles contacts within different .VCF files. You can go ahead and share the .VCF files with who ever you want, all they need to do is import it.

To import the contact/circle information goto Circles and click on Find People, Import Address Book.. select the shared .VCF file. You will have those contacts in a selection list with a small icon next to each one. Simply create a new circle and drag them in.

Bear in mind, more details about your contacts other than their email address and name will be shared if you have such information in your contact list.