Speaking from experience both working under and being a Scrum Master developer... yes, yes they can.
While it is a bad idea for the Scrum Master to also be the Product Owner (since they have occasionally contradictory roles), the Scrum Master role aligns with the role of Developer fairly well.
As per the Scrum Guide, the Scrum Master's duties to the Development Team include:
- Coaching the Development Team in self-organization and
- Helping the Development Team to create high-value products;
- Removing impediments to the Development Team’s progress;
- Facilitating Scrum events as requested or needed; and,
- Coaching the Development Team in organizational environments in which
Scrum is not yet fully adopted and understood.
None of those present any significant impediments to a Developer that would not be present for a dedicated Scrum Master (aside from a bit of split focus between Scrum Master duties and actual development work, which could somewhat hinder a single developer - you).
Technically speaking, you don't need a certification to become a Scrum Master - if you perform the duties of a Scrum Master, and are acknowledged as a Scrum Master by the team, then you are a Scrum Master. While a certification is helpful for learning the basics and proving to employers that you are competent, as with everything else, experience is the best teacher. If you want to get up to snuff as quickly as possible (aside from just diving in head-first), the best route is to learn directly from an experienced Scrum Master, though readings can prove invaluable as well - Niels van Reijmersdal provided several useful ones already.