  We investigate the feasibility of measuring weak gravitational lensing using
21cm intensity mapping with special emphasis on the performance of the planned
Square Kilometre Array (SKA). We find that the current design for SKA-Mid
should be able to measure the evolution of the lensing power spectrum at z~2-3
using this technique. This will be a probe of the expansion history of the
universe and gravity at a unique range in redshift. The signal-to-noise is
found to be highly dependent on evolution of the neutral hydrogen fraction in
the universe with a higher HI density resulting in stronger signal. With
realistic models for this, SKA Phase 1 should be capable of measuring the
lensing power spectrum and its evolution. The signal-to-noise's dependence on
the area and diameter of the telescope array is quantified. We further
demonstrate the applications of this technique by applying it to two specific
coupled dark energy models that would be difficult to observationally
distinguish without information from this range of redshift. We also
investigate measuring the lensing signal with 21cm emission from the Epoch of
Reionization (EoR) using SKA-Low and find that it is unlikely to constrain
cosmological parameters because of the small survey size, but could provide a
map of the dark matter within a small region of the sky.
