It seems this is impossible.
Chrome iOS wont open a vcf file as far as I can tell and I've tried many possible solutions.
Mobile Safari will open a vcf with the Add Contact screen but there is no way that I can see that you can explicitly open a link in mobile Safari from Chrome.
The best solution I can come up with is clicking the link copies it, then opens a popup which tells the user to switch to safari and paste the link in there.