We present a novel label-free method of quantifying single stranded DNA concentrations in solution using the Liquid Core Optical Ring Resonator (LCORR). The LCORR is a glass capillary that is capable of evanescent sensing of analytes while providing fluidic delivery through its hollow core. An evanescent field is excited in the ring-shaped circumference of the LCORR by externally coupled photons, which circulate via total internal reflection in the form of Whispering Gallery Modes (WGM's). When the wall of the capillary is etched to under 5 um, the evanescent field from the WGM's is exposed in both the internal and external media. Chemical modification of the interior of the LCORR enables specific capture of target oligonucleotides by hybridization with a covalently bound probe. Refractive index changes at this interface are shown to produce a measurable change in the optical signal by shifting the resonance condition of the cavity. Real time kinetic analysis of the hybridization between the two complimentary strands is demonstrated as well as a thorough calibration of the sensor response to strand lengths between 25 and 100 bases and bulk concentration from 0.5 nM to 10 uM. Non-specific binding of completely mismatched oligonucleotides is shown to be minimal and single base mismatch detection is also demonstrated definitively.