Optical trapping has become an optimal choice for biological research at the microscale due to its non-invasive performance and accessibility for quantitative studies, especially on the forces involved in biological processes. However, reliable force measurements depend on the calibration of the optical traps, which is different for each experiment and hence requires high control of the local variables, especially of the trapped object geometry. Many biological samples have an elongated, rod-like shape, such as chromosomes, intracellular organelles (e.g., peroxisomes), membrane tubules, certain microalgae, and a wide variety of bacteria and parasites. This type of samples often requires several optical traps to stabilize and orient them in the correct spatial direction, making it more difficult to determine the total force applied. Here, we manipulate glass microcylinders with holographic optical tweezers and show the accurate measurement of drag forces by calibration-free direct detection of beam momentum. The agreement between our results and slender-body hydrodynamic theoretical calculations indicates potential for this force-sensing method in studying protracted, rod-shaped specimens.