We demonstrate cryogenic, electrically-injected, waveguide-coupled Si light-emitting diodes (LEDs) operating at 1.22 $mu$m. The active region of the LED consists of W centers implanted in the intrinsic region of a $p$-$i$-$n$ diode. The LEDs are integrated on waveguides with superconducting nanowire single-photon detectors (SNSPDs). We demonstrate the scalability of this platform with an LED coupled to eleven SNSPDs in a single integrated photonic device. Such on-chip optical links may be useful for quantum information or neuromorphic computing applications.