We study the effect of oblique illumination on the functioning of a plasmonic nanoantenna for chiral light. The antenna is designed to receive a structured beam of light and produce a nanosized near-field distribution that possesses non-zero orbital angular momentum. The design consists of metal (gold) micro-rods laid on a dielectric surface and is compatible with well-developed nanofabrication techniques. Experimental arrangements often require such an antenna to operate in a tilted geometry, where input light is incident on the antenna at an oblique angle. We analyze the limitations that the angled illumination imposes and discuss approaches to mitigate these limitations. Through our numerical simulations, we find that tilt angles larger than 30 degrees require modifications to the antenna design. Our analysis guides current and future experimental configurations to pushing the limits of resolution and sensitivity.