Solar telescope is the primary means of carrying out high-resolution solar observations and advanced heliophysical research, while adaptive optics has become requisite technology to address the limitations of the atmosphere turbulence in terms of imaging resolution. However, in previous works, the adaptive optics system was designed independently behind the solar telescope, which makes the system large and complex, with low transmittance and significant instrumental polarization, thus limiting the performance of solar telescopes. Here, we develop a novel and ultra-compact solar telescopes with wavefront correction ability, called solar adaptive optics telescope (SAOT), which hides the adaptive optics system into the solar telescope. The proposed full-wavefront measurement method obtains the global tip-tilt and higher-order wavefront aberrations synchronously by using only one Hartmann-Shack wavefront sensor, which are corrected by the only secondary deformable mirror (SDM) simultaneously. As a result, the presented SAOT looks like a simple solar telescope, but it has comprehensive wavefront correction and fine tracking ability, significantly improving system integration, transmission efficiency, and even reliability while reducing instrumental polarization. A 600 mm prototype of SAOT is also built and can realize high-resolution observation of the solar photosphere layer in the sky. The numeric simulations, experiments, and observing results verify the validity and feasibility of the presented SAOT method, and the successful development and observation of SAOT, which marks a significant milestone in the field, offers valuable insights for the future advancement of large solar telescopes.