We present a new measurement of the \alpha -spectroscopic factor ( S _ { \alpha } ) and the asymptotic normalization coefficient ( ANC ) for the 6.356 MeV 1/2 ^ { + } subthreshold state of ^ { 17 } O through the ^ { 13 } C ( ^ { 11 } B , ^ { 7 } Li ) ^ { 17 } O transfer reaction and we determine the \alpha -width of this state . This is believed to have a strong effect on the rate of the ^ { 13 } C ( \alpha , n ) ^ { 16 } O reaction , the main neutron source for slow neutron captures ( the s -process ) in asymptotic giant branch ( AGB ) stars . Based on the new width we derive the astrophysical S-factor and the stellar rate of the ^ { 13 } C ( \alpha , n ) ^ { 16 } O reaction . At a temperature of 100 MK our rate is roughly two times larger than that by Caughlan & Fowler ( 7 ) and two times smaller than that recommended by the NACRE compilation . We use the new rate and different rates available in the literature as input in simulations of AGB stars to study their influence on the abundances of selected s -process elements and isotopic ratios . There are no changes in the final results using the different rates for the ^ { 13 } C ( \alpha , n ) ^ { 16 } O reaction when the ^ { 13 } C burns completely in radiative conditions . When the ^ { 13 } C burns in convective conditions , as in stars of initial mass lower than \sim 2 M _ { \sun } and in post-AGB stars , some changes are to be expected , e.g. , of up to 25 % for Pb in our models . These variations will have to be carefully analyzed when more accurate stellar mixing models and more precise observational constraints are available .