Robots capable of hover flight in constrained indoor environments have many applications, however their range is constrained by the high energetic cost of airborne locomotion. Perching allows flying robots to scan their environment without the need to remain aloft. This paper presents the design of a mechanism that allows indoor flying robots to attach to vertical surfaces. To date, solutions that enable flying robot with perching capabilities either require high precision control of the dynamics of the robot or a mechanism robust to high energy impacts. We propose in this article a perching mechanism comprising a compliant deployable pad and a passive self-alignment system, that does not require any active control during the attachment procedure. More specifically, a perching mechanism using fibre-based dry adhesives was implemented on a 300~g flying platform. An adhesive pad was first modeled and optimized in shape for maximum attachment force at the low pre-load forces inherent to hovering platforms. It was then mounted on a deployable mechanism that stays within the structure of the robot during flight and can be deployed when a perching maneuver is initiated. Finally, the perching mechanism is integrated onto a real flying robot and successful perching maneuvers are demonstrated as a proof of concept.