Shell-model calculations of solar neutrino absorption cross sections for ⁴⁰Ar, the proposed component of the ICARUS detector, are presented. It is found that low-lying Gamow-Teller transitions lead to a significant enhancement of the absorption rate over that expected from the Fermi transition between the isobaric analog states, leading to an overall absorption cross section for ⁸B neutrinos of (11.5 ± 0.7) × 10⁻⁴³ cm² or a total expected rate of 6.7 ± 2.5 SNU. We also note that the pertinent Gamow-Teller transitions in ⁴⁰Ar are experimentally accessible from the β-decay of the mirror nucleus ⁴⁰Ti. Predictions for the branching ratios to states in ⁴⁰Sc are presented, and the theoretical halflife of 55 ± 5 ms is found to be in good agreement with the experimental value of 56₋₁₂⁺¹⁸ ms.