We report the first detection on Titan of the small cyclic molecule cyclopropenylidene (c-C3H2) from high sensitivity spectroscopic observations made with the Atacama Large Millimeter/sub-millimeter Array (ALMA). Multiple lines of cyclopropenylidene were detected in two separate datasets: ~251 GHz in 2016 (Band 6) and ~352 GHz in 2017 (Band 7). Modeling of these emissions indicates abundances of 0.50 +/- 0.14 ppb (2016) and 0.28 +/- 0.08 (2017) for a 350 km step model, which may either signify a decrease in abundance, or a mean value of 0.33 +/- 0.07 ppb. Inferred column abundances are (3-5)E12 cm-2 in 2016 and (1-2)E12 cm-2 in 2017, similar to photochemical model predictions. Previously the C3H3+ ion has been measured in Titans ionosphere by Cassinis Ion and Neutral Mass Spectrometer (INMS), but the neutral (unprotonated) species has not been detected until now, and aromatic versus aliphatic structure could not be determined by the INMS. Our work therefore represents the first unambiguous detection of cyclopropenylidene, the second known cyclic molecule in Titans atmosphere along with benzene (C6H6) and the first time this molecule has been detected in a planetary atmosphere. We also searched for the N-heterocycle molecules pyridine and pyrimidine finding non-detections in both cases, and determining 2-{sigma} upper limits of 1.15 ppb (c-C5H5N) and 0.85 ppb (c-C4H4N2) for uniform abundances above 300 km. These new results on cyclic molecules provide fresh constraints on photochemical pathways in Titans atmosphere, and will require new modeling and experimental work to fully understand the implications for complex molecule formation.