In this paper, we present MOBI-COG which is an application that runs on a mobile device, such as a tablet or a smartphone, and provides an automated and instant dementia screening service. The MOBI-COG App is a complete automation of a widely used 3- minute dementia screening test called the Mini-Cog test, which is administered by primary caregivers for a quick screening of dementia in elderly. Besides asking the patient to remember and then recall a set of three words, the test involves a free-hand clock drawing test. The MOBI-COG App automates all these steps - including the automatic assessment of the correctness of a clock drawn on the touch screen of a mobile device. We train the MOBI-COG App with over 1000 touch-drawn clocks and show that the system is capable of detecting and recognizing digits in less than 100 ms, in-situ (i.e. without the help of any back-end server), with 99.53% accuracy, and is robust to changes in people, sizes of the drawn digits, and screen sizes of the mobile devices. We perform a usability study of MOBI-COG involving eight healthy human subjects and show that the system is capable of performing all three steps of the test effectively. We also provide a summary of the users' comments on the application.