Manual SPI interface on Raspberry PI
The MCP4131 uses an annoying "multiplexed" SPI implementation.



To write to the MCP4131, you cannot just write 8 bits. You need to write 16 bits.  They are described in the datasheet.



You will want to use address 0 (Volatile wiper #0) and command 0, with the data being your value prefixed by zeroes. In other words, clock out eight zero bits before your value and you'll be OK.



I wish Microchip didn't put all their SPI digital pots into one datasheet.  It makes the datasheet harder to read.

Also, double check the voltage across P0A and P0B (the ends of the resistor).  If you don't have voltage there, changing the pot tap won't change the wiper voltage.