In this work, tunable MEMS capacitors are realized using a vertically grown carbon nanotube array. The vertical CNT array forms an effective CNT membrane, which can be electrostatically actuated like the conventional metal plates used in MEMS capacitors. The CNT membrane is grown on titanium nitride metal lines, with a Al/Fe bi-layer as buffer layer and catalyst material respectively, using chemical vapor deposition process. Two different anchor configurations are investigated. A maximum capacitance of 400 fF and maximum tunability of 5.8% is extracted from the S-parameter measurements. Using the tunable MEMS vertical array capacitor a voltage controlled oscillator (VCO) is demonstrated showing promise for integrating CNTs for communications applications.