Only one USB-C port will charge my MacBook Pro?
So, to summarize, the port works for all functions (USB connectivity, display, etc) including charging downstream devices (like a smartphone), but you cannot charge the MacBook.


Your SMC chip needs to be reset.  Hold ^ Control⇧ Shift⌥ Option ⦿ Power from a powered off state.
There is failed component in the charging circuitry.  


USB 3.1 (power delivery) negotiates power.  When you connect your power adapter to the port, it basically says "I'm a power adapter and I can charge."  The device (MacBook) will respond "I need X" and will negotiate with adapter for what can be delivered.  Once negotiated, the adapter sends the power and the USB port passes it to the charging circuit (handled by the SMC)

What could be happening here is one of two things:


The port is no longer negotiating for power (unlikely because the port still functions otherwise
The charging circuitry physically isn't getting the power (a broken electrical path)


If the SMC reset doesn't fix, take it in for service.