The dual-comb technique is a powerful tool in industrial inspection and scientific research and is capable of realizing ultrahigh-resolution and fast broadband spectral measurements. We propose an absolute angular-position measurement method based on dual-comb spectroscopy. With a simple layout, the absolute angular position can be naturally determined through the traceable and wide-amplitude spectra of the autocollimation diffracted beams of the target grating. We experimentally demonstrate that a precision of 0.12 arcsec in the dynamic range of approximately 6660 arcsec, along with a 1 kHz repetition rate difference, is achieved. Compared with a commercial autocollimator, over 1000 arcsec, the comparison residuals are kept within ±0.3 arcsec.