Acousto-optic interactions, employed in the ultrafast laser regulation, possess remarkable advantages for fast tuning performance in a wide spectral range. Here, we propose an ultrafast fiber laser whose wideband tunability is provided by an acousto-optic structure fabricated with an etched single-mode fiber. Because of the laser polarization conversion induced by the coupling between the core and cladding vector modes in the etched fiber, a band-pass characteristic of the acousto-optic interaction is achieved to effectively regulate the inner-cavity gain range. Cooperating with a saturable absorber based on single-wall carbon nanotubes (SWCNTs) with polarization robustness, a soliton operating state is achieved in the tunable erbium-doped fiber laser. By controlling the acoustical wave frequency from 1.039 to 1.069 MHz, this soliton laser can be conveniently tuned in a wide spectral range from 1571.52 to 1539.26 nm. Meanwhile, the laser pulses have near-transform-limited durations stably maintaining less than 2 ps at different wavelength channels, owing to the broadband nonlinear absorption of SWCNTs.