We investigate the nonlinear optical phenomenon of self-focusing in air with phase-stabilized few-cycle light pulses. This investigation looks at the role of the carrier-envelope phase by observing a filament in air, a nonlinear phenomenon that can be utilized for few-cycle pulse compression [ Appl. Phys. B 79, 673 (2004) ]. We were able to measure the critical power for self-focusing in air to be $18\pm 1\text{\hspace{0.17em} GW}$ for a 6.3 fs pulse centered at 800 nm. Using this value and a basic first-order theory, we predicted that the self-focusing distance should deviate by $790\mu \text{m}$ as the carrier-envelope phase is shifted from 0 to $\pi /2\text{\hspace{0.17em} rad}$ . In contrast, the experimental results showed no deviation in the focus distance with a $3\sigma$ upper limit of $180\mu \text{m}$ . These counterintuitive results show the need for further study of self-focusing dynamics in the few-cycle regime.