Just 500 units of the car - 120 destined for the UK market - have been made available to order through the social networking site, with reports suggesting stocks are selling out fast.
Priced from £16,995, the EcoSport limited edition is available with either a 123bhp 1.0-litre EcoBoost engine or a 90bhp 1.5-litre diesel engine.
The limited-edition models also include an expanded version of Ford's Sync AppLink infotainment system, which benefits from new apps and functionality.
Autoread is perhaps the biggest addition to the system. The programme, available on iOS and android devices, reads out emails and text messages and allows users to dictate replies via the car's voice-recognition service.
Elsewhere, TomTom has signed up to provide satellite-navigation coverage, while motorists can also use voice-activation to book hotel rooms via the new Hotels.com app. Nearby events are also displayed thanks to a Wcities Eventseeker app.
Over 5000 developers are already registered to help improve the open-source software, with other car manufacturers invited to use the service.
Director of Ford electronics and electrical systems Jim Buczkowski said: ""The opportunity is to embrace the creativity that exists out there with the app development community.
"You can talk a lot about creating a closed standard but the truth is you spend a lot of time protecting what you've created. Platforms are a really great way to move quickly. You open it up and allow that creativity to let you move very quickly.