In this paper we have reported the synthesis of high quality vertically aligned undoped and Mn-doped ZnO single crystalline nanorods arrays on Si (100) substrates using two steps process, namely, initial slow seed layer formation followed by solution growth employing wet chemical hydrothermal method. The shapes of the as grown single crystalline nanorods are hexagonal. The diameter and length of the as grown undoped ZnO nanorods varies in the range of 80-150 nm and 1.0 - 1.4 μm, respectively. Along with the lattice parameters of the hexagonal crystal structure, the diameter and length of Mn doped ZnO nanorods are found to increase slightly as compared to the undoped ZnO nanorods. The X-ray photoelectron spectroscopy confirms the presence of Mn atoms in Mn2+ state in the single crystalline ZnO nanorods. The recorded photoluminescence spectrum contains two emissions peaks having UV exciton emissions along with a green-yellow emission. The green-yellow emissions provide the evidence of singly ionized oxygen vacancies. The magnetic field dependent magnetization measurements [M (H)] and zero field cooled (ZFC) and field cooled (FC) magnetization [M(T)] measurements have been carried out at different isothermal conditions in the temperature range of 5-300 K. The Mn doped ZnO nanorods clearly show room temperature ferromagnetic ordering near room temperature down to 5 K. The observed magnetization may be attributed to the long range ferromagnetic interaction between bound magnetic polarons led by singly charged oxygen vacancies.