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A new ro-vibrational line list for the ground electronic state of the main isotopologue of acetylene, $^{12}$C$_2$H$_2$, is computed as part of the ExoMol project. The aCeTY line list covers the transition wavenumbers up to 10,000 cm$^{-1}$ ($ \lambda >1$ $\mu$m), with lower and upper energy levels up to 12,000 cm$^{-1}$ and 22,000 cm$^{-1}$ considered, respectively. The calculations are performed up to a maximum value for the vibrational angular momentum, $K_{\rm max}=L_{\rm max}$ = 16, and maximum rotational angular momentum, $J$ = 99. Higher values of $J$ were not within the specified wavenumber window. The aCeTY line list is considered to be complete up to 2200 K, making it suitable for use in characterising high-temperature exoplanet or cool stellar atmospheres. Einstein-A coefficients, which can directly be used to calculate intensities at a particular temperature, are computed for 4.3 billion (4,347,381,911) transitions between 5 million (5,160,803) energy levels. We make comparisons against other available data for $^{12}$C$_2$H$_2$, and demonstrate this to be the most complete line list available. The line list is available in electronic form from the online CDS and ExoMol databases.