Carboxylic acid groups were introduced into polystyrene, and the effect both on melt rheology and on mechanical properties of stretched and quenched anisotropic solids below the glass transition temperature (Tg) was investigated. First, the facile preparation of well-defined copolymers of styrene (S) and 4-vinylbenzoic acid (A) by reversible addition−fragmentation chain-transfer (RAFT) polymerization was demonstrated. The evaluation of monomer reactivity ratios shows that the acid polymerizes faster than styrene but that block formation is suppressed under the applied conditions. Addition of acid groups leads to an increase in Tg and this is documented by the detection of acid dimers in the glassy polymers. Importantly, linear viscoelastic (LVE) measurements confirm that all the tested samples have a similar number of entanglements per chain (Z), which suggests that the acid groups do not form hydrogen bonds at temperatures above Tg. These are further confirmed by non-linear extensional rheology of the samples in uniaxial extensional flow. Stretching melts of these polymers at a rate faster than the inverse Rouse time, followed by rapid quenching below Tg leads to polymer fibers that remain highly flexible in analogy with non-modified polystyrene. However, the resulting acid-containing polymer fibers have higher yield stress and ductility at room temperature compared to the non-modified polystyrene fibers. This approach presents a facile route to improve mechanical properties of anisotropic glassy polystyrene.