The nitrogen-vacancy (NV) color center in diamond is gaining significant interest for applications in nanoscale sensing. The optical addressability of the magnetically sensitive spin states and the ability to coherently control these states at room temperature makes this system an exciting candidate for spin-based magnetometry. I constructed an optical tweezers apparatus combined with a confocal fluorescence apparatus. Using the optical apparatus, we demonstrate three-dimensional position control of nanodiamonds in solution with simultaneous readout of ground-state electron-spin resonance (ESR) transitions in an ensemble of diamond nitrogen-vacancy (NV) color centers. Despite the motion and random orientation of NV centers suspended in the optical trap, we observe distinct peaks in the measured ESR spectra qualitatively similar to the same measurement in bulk. Accounting for the random dynamics, we model the ESR spectra observed in an externally applied magnetic field to enable dc magnetometry in solution. We estimate the dc magnetic field sensitivity based on variations in ESR line shapes to be approximately 45 microTesla/Hz½. This technique may provide a pathway for spin-based magnetic, electric, and thermal sensing in fluidic environments and biophysical systems inaccessible to existing scanning probe techniques.