The drill has begun at a geologically interesting location nicknamed "The Kimberley".
In this selfie, Curiosity appears to be leaning its "head" - a suite of instruments including the Chemcam and Mastcam cameras to the side - capturing the 5 km high Aeolis Mons ('Mount Sharp') on the horizon.
In coming days, the rover will conduct a preparatory "mini-drill" operation to check the area for readiness, Nasa's Jet Propulsion Laboratory said in a statement.
The hammering drill on Curiosity collects powdered sample material from rocks and then delivers portions to laboratory instruments onboard.
The self-portrait has been put together by Discovery News.
Last month, Nasa in partnership with New York-based hardware startup LittleBits launched a space kit that enables users to build their own Mars Rovers at a school or college lab or at home.
The kit comes with 12 "bit modules" that provide things like power, remote triggering, light sensing and motorisation.
In collaboration with Nasa's Goddard Space Flight Center, LittleBits also came up with 10 activities that allow users to build everything from a satellite dish to a miniature Mars Rover.
"Our mission is to allow anyone to create their own hardware, to make playing with electronics more like playing with Legos," Ayah Bdeir, founder and CEO of LittleBits, was quoted as saying.
The kit costs $189 (roughly Rs. 11,300) and users can buy it online from the LittleBits website.
Written with inputs from IANS