How to Attach a vCard in Gmail
1) In contacts, click on the contact you would like to attach in an email. Then click on More > Export.
2) Then click on the “selected contacts” radio button and choose “vCard format”
3) Click on Export
4) Google Chrome will download the .vcf file into your downloads folder and will display the file in the bottom toolbar
5) When composing an email, you can click on the paperclip icon to attach the downloaded .vcf file.