A continuous-wave all-solid-state tunable Ti:sapphire laser with compact configuration is presented. The frequency-tuning range extends from 760 to 825 nm by rotating the birefringent filters. When the intracavity etalon is locked on the oscillating frequency of the laser and the length of the resonator is scanned by the piezoelectric ceramics transducer, a maximal continuous frequency-tuning range of 15.3 GHz is realized. The obtained Ti:sapphire laser is successfully applied to scan the saturation absorption spectroscopy of $D_1$ transitions of ${}^{87}\mathrm{Rb}$ atoms around the wavelength of 794.97 nm.