The potential importance of the angular momentum which is gained by accreting white dwarfs (WDs) has been increasingly recognized in the context of Type Ia supernova (SN Ia) single-degenerate model. The expectation that the spin of the WD can delay the explosion should help the single-degenerate model to be consistent with the observed properties of most SNe Ia, in particular by avoiding hydrogen contamination. In this paper, we attempt to study the most prominent single-degenerate supersoft (WD + MS) channel when the rotation of accreting WDs is considered. We present a detailed binary population synthesis study to examine the predicted population of SNe Ia for this channel. For our standard model, we find that 77 per cent of these SNe Ia explode with WD masses which are low enough to be supported by solid-body rotation ( ≤ 1.5 M⊙); this is a substantially higher proportion than found by previous work. Only 2 per cent have WD explosion masses ≥2.0 M⊙; these require the initial WD mass to be larger than 1.0 M⊙. We further discuss the possible origin of the diversity of SNe Ia from the pre- and post-accretion properties of the WDs in this population. We also suggest that some SN Ia progenitors with substantial circumstellar hydrogen, including some apparent Type IIn SNe, might be related to WDs which required support from differential rotation to avoid explosion, since these can still be accreting from hydrogen-rich donors with a relatively high mass-transfer rate at the time of the SN explosion.