  We report on the first demonstration of fluorescence detection using
single-photon avalanche photodiodes (SPADs) monolithically integrated with a
microfabricated surface ion trap. The SPADs are positioned below the trapping
positions of the ions, and designed to detect 370 nm photons emitted from
single $^{174}$Yb$^+$ and $^{171}$Yb$^+$ ions. We achieve an ion/no-ion
detection fidelity for $^{174}$Yb$^+$ of 0.99 with an average detection window
of 7.7(1) ms. We report a dark count rate as low as 1.2 kHz at room temperature
operation. The fidelity is limited by laser scatter, dark counts, and heating
that prevents holding the ion directly above the SPAD. We measure count rates
from each of the contributing sources and fluorescence as a function of ion
position. Based on the active detector area and using the ion as a calibrated
light source we estimate a SPAD quantum efficiency of 24$\pm$1%.
