Molecular motors in cells typically produce highly directed motion; however, the aggregate, incoherent effect of all active processes also creates randomly fluctuating forces, which drive diffusive-like, nonthermal motion. Here, we introduce force-spectrum-microscopy (FSM) to directly quantify random forces within the cytoplasm of cells and thereby probe stochastic motor activity. This technique combines measurements of the random motion of probe particles with independent micromechanical measurements of the cytoplasm to quantify the spectrum of force fluctuations. Using FSM, we show that force fluctuations substantially enhance intracellular movement of small and large components. The fluctuations are three times larger in malignant cells than in their benign counterparts. We further demonstrate that vimentin acts globally to anchor organelles against randomly fluctuating forces in the cytoplasm, with no effect on their magnitude. Thus, FSM has broad applications for understanding the cytoplasm and its intracellular processes in relation to cell physiology in healthy and diseased states.