Now you can do so through Bandai's latest Jibun Damashii (自分魂).
Well, not exactly everyone that is. At the moment, Jibun Damashii is going to be limited through web order, which most probably means it's limited to Japan as well. Then again, Bandai's is testing on the acceptance of this new "service" I believe, so there's a good chance that it will be promoted to mainstream merchandise list.
Anyway, Jibun Damashii is the customization of your own portrait to become the sculpture of the face of an S.I.C. Kamen Rider the First. You can choose between a normal face or a round-type face to be used (フェイスベースは普通顔と丸顔の2種類を用意。). Not quite sure what that means myself ^^;
The bike shown is not included.
The package also comes with a display base customized with the customer's own name or any text preferred. Even the figure packaging can be customized with your name. ^^ Two kinds of masks included: full and half showing the mouth.
Registration is required to order this service. Once an order is placed, cancellation is not available. However, details of how the pre-order process is not available at the moment.
June 26th release, 13,650 Yen (inclusive of tax).
Images and information from Jibun Damashii.