Can you record a microphone into a Schiit Modi+?
No. A DAC is a one-way street: this one lists zero analogue inputs, 0 dB of gain and no phantom power. Its USB, optical and coax sockets are digital sources feeding it, not places to record into.
Short answer: no, and no cable or adapter changes that. The Modi+ has no microphone input, no preamp and no analogue-to-digital converter.
A DAC converts digital to analogue. That is the whole device: digital arrives over USB, Toslink or coax, analogue leaves over RCA. Its specification in this catalogue makes the point without ambiguity — analogue inputs: none; maximum gain: 0 dB; phantom power: not provided. There is no jack to record into, because recording requires the opposite conversion, and the Modi+ does not contain the circuit that performs it.
The confusion is caused by a word. The Modi+ has three connectors labelled "input", and all three are digital sources being fed to the DAC, not entry points for your voice. The sockets that carry audio you can hear — RCA and the headphone jack on a stacked amp — are outputs. Reading the back panel of a DAC as if it were a mixer leads directly to this question.
What to do instead: keep the DAC for listening and add an audio interface for recording. The two live side by side on the same computer — the interface presents itself as an input device, the Modi+ as an output device, and the operating system routes them independently. Do not try to feed the interface's line outputs into the Modi+ on the way to your headphones: there is no analogue input to feed, and even the digital path would need an S/PDIF output that entry-level interfaces do not have.
The useful giveaway for any box you are unsure about: look for the phantom power line and the gain figure. A device that publishes neither has no microphone preamp, and a device with no microphone preamp was never intended to hear anything.