Graphene is a mechanically robust 2D material promising for flexible optoelectronic applications. However, its electromagnetic properties under strain are experimentally poorly understood. Here we present the far-infrared transmission spectra of large-area chemical-vapor deposited monolayer graphene on a polyethylene terephthalate substrate subjected to uniaxial strain. The effective strain value is calibrated using the Raman spectroscopy and corrected for a relaxation of wrinkles and folds seen directly by atomic-force microscopy. We find that while the Drude weight and the Fermi level remain constant, the scattering rate increases by more than 10% per 1% of applied strain, showing a high level of reproducibility during strain cycling. As a result, the electronic mobility and optical absorption of graphene at terahertz and lower frequencies appear to also be sensitive to strain, which opens pathways to control these key parameters mechanically. We suggest that such a functionality can be potentially used in flexible optoelectronic and microelectromechanical systems based on graphene. By combining our findings with existing theoretical models, we discuss the possible mechanisms of strain-controlled Drude scattering.