Electrospinning provides an effective methodology to obtain high aspect ratio polymer fibers for biomimetic applications. In this article, we evaluate the effect of topology on adhesion between aligned fibers. Polycaprolactone is electrospun using two different setups: (i) a tip collector and (ii) a flat collector. The tip collector enables the fibers to self-align. When a fiber reaches the tip collector, the next fiber is repelled by the charge they carry, forcing the fibers to deposit in a parallel arrangement. The flat collector allows the fibers to deposit at random. The adhesion between the fiber mats is measured using a T-peel test. Adhesion strength (758.7 ± 211.7 kPa) changes marginally with the peeling rate and applied pressure on the membranes. Aligned fibers exhibit higher adhesion strength between the membranes in comparison to randomly oriented nonwovens (613.1 ± 79.9 kPa). The estimated Johnson–Kendall–Roberts contact energy (83.1 ± 32.5 mJ/m2) is consistent with the range of van der Waals adhesion forces. This work shows how the adhesion between two polymer membranes can be modulated by surface topology, based on a T-peel testing setup.