An efficient turn-on fluorescence probe for biomolecules not only helps in its sensitive detection but is also useful to understand the different interactions that are operating between biomolecules and probes. Polycyclic aromatic molecules are known to be strong interacting ligand for DNA and extensively studied as a model cancer drug. However, these molecules show large decrease in their emission intensity, i.e., a turn-off probe for DNA. In the present work, we have synthesized a benzothiazole-based anthracene derivative and studied its interaction with a natural DNA with the aim of having a turn-on DNA probe with a polycyclic aromatic moiety. Our detailed spectroscopic studies show that the new probe strongly interacts with DNA molecules and results in a significant increase in its emission yield. Time-resolved studies show a large increase in probe's excited-state lifetime in DNA solution. Detailed experiments have been performed to understand its mode of interaction with DNA molecules. The mode of interaction has also been supported by the blind molecular docking studies. Further, the viscosity-dependent photophysical properties and detailed quantum chemical calculations confirm that the new probe belongs to molecular rotor class of molecules. Association with DNA molecules results in a significant retardation in the nonradiative deactivation process due to the torsional motion in the excited state of the probe and leads to a significant increase in its emission yield. Thus, due its molecular rotor nature, despite with a turn-off fluorophore unit, anthracene, the new probe, acts as a sensitive turn-on fluorescence probe for DNA molecules.