We describe a custom time-to-digital converter (TDC) designed to time tag individual photons from multiple single photon detectors with high count rate, continuous data logging and low systematics. The instrument utilizes a taped-delay line approach on an FPGA chip which allows for sub-clock resolution of <100 ps. We implemented our TDC on a Re-configurable Open Architecture Computing Hardware Revision 2 (ROACH2) board which allows continuous data streaming and time tagging of up to 20 million events per second. The functioning prototype is currently set up to work with up to ten independent channels. We report on the laboratory characterization of the system, including RF pick up and mitigation as well as measurement of in-lab photon correlations from an incoherent light source (artificial star). Additional improvements to the TDC will also be discussed, such as improving the data transfer rate by a factor of 10 via an SDP+ Mezzanine card and PCIE 2SFP+ 10 Gb card, as well as scaling to 64 independent channels.