We have characterized the spectroscopic orbit of the TWA 3A binary and provide preliminary families of probable solutions for the TWA 3A visual orbit, as well as for the wide TWA 3A-B orbit. TWA 3 is a hierarchical triple located at 34 pc in the similar to 10 Myr old TW Hya association. The wide component separation is 1."55; the close pair was first identified as a possible binary almost 20 years ago. We initially identified the 35-day period orbital solution using high-resolution infrared spectroscopy that angularly resolved the A and B components. We then refined the preliminary orbit by combining the infrared data with a reanalysis of our high-resolution optical spectroscopy. The orbital period from the combined spectroscopic solution is similar to 35 days, the eccentricity is similar to 0.63, and the mass ratio is similar to 0.84; although this high mass ratio would suggest that optical spectroscopy alone should be sufficient to identify the orbital solution, the presence of the tertiary B component likely introduced confusion in the blended optical spectra. Using millimeter imaging from the literature, we also estimate the inclinations of the stellar orbital planes with respect to the TWA 3A circumbinary disk inclination and find that all three planes are likely misaligned by at least similar to 30 degrees. The TWA 3A spectroscopic binary components have spectral types of M4.0 and M4.5; TWA 3B is an M3. We speculate that the system formed as a triple, is bound, and that its properties were shaped by dynamical interactions between the inclined orbits and disk.