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This work describes the design and implementation of optics for EXCLAIM, the EXperiment for Cryogenic Large-Aperture Intensity Mapping. EXCLAIM is a balloon-borne telescope that will measure integrated line emission from carbon monoxide at redshifts z < 1 and ionized carbon ([CII]) at redshifts z = 2.5 - 3.5 to probe star formation over cosmic time in cross-correlation with galaxy redshift surveys. The EXCLAIM instrument is designed to observe at frequencies of 420-540 GHz using six microfabricated silicon integrated spectrometers with spectral resolving power R = 512 coupled to kinetic inductance detectors. A completely cryogenic telescope cooled to a temperature below 5 K provides low-background observations between narrow atmospheric lines in the stratosphere. Off-axis reflective optics use a 90-cm primary mirror to provide 4.2' full-width at half-maximum resolution at the center of the EXCLAIM band over a field of view of 22.5'. Illumination of the 1.7 K cold stop combined with blackened baffling at multiple places in the optical system ensures low (<-40 dB) edge illumination of the primary to minimize spill onto warmer elements at the top of the dewar., (© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC) license (https://creativecommons.org/licenses/by-nc/4.0/).)