Control the digital potentiometer MCP4151 from your Arduino.

Since this library only uses three general purpose digital I/O pins, at the moment there is no compatibility issue foreseen with any model of Arduino. If you notice some incompatibility however, feedback is welcome.

#include <MCP4151.h>

MCP4151 mcp4151(2,3,4);

void setup() {
    mcp4151.begin()
    mcp4151.setWiper(128); // set potentiometer mid-point
}

void loop() {}

The above code only will be of use if you first hook up the circuitry correctly, which is now explained:

The MCP4151 is no classical SPI device with 4-wire SPI. Instead, 3-wire SPI has been chosen by the designers. The datasheet proposes interfacing 4 pins of the master/controller side 4-wire SPI device (Arduino) with 3 pins of the 3-wire MCP4151. However, do not do this if you use this library. This lib implements real 3-wire SPI also on Arduino side. So you only need 3 wires sticking to your Arduino. Yay! Read on.

As seen in the introductory code snippet:

MCP4151 mcp4151(2,3,4)

There are three pins of the Arduino chosen at random/your choice:

• 2 is chosen as CS pin in the example code
• 3 is chosen as SCK pin in the example code
• 4 is chosen as SDIO pin in the example code

You can choose any three pins of the Arduino, as long as they can be digital outputs aka pinMode(PIN, OUTPUT) and digitalWrite(PIN, HIGH/LOW) work normally on your chosen Arduino pins.
You then just connect the pins of Arduino with the pins with corresponding role on the MCP4151 (CS to CS, SCK to SCK), except that the chosen pin for SDIO transfer (pin 4 in the code example above) MUST be connected via a resistor to the SDIO pin of the MCP4151. For example I chose 330Ohm and it worked. 1kOhm did not work for me by the way.
This section has been talking about the pins that take part in data transfer. On the MCP4151 these are the pins CS, SCK and SDIO (pins 1 through 3). The next section talks about the three pins that comprise the electrical potentiometer interface of the MCP4151, which are P0A, P0W and P0B (pins 5 through 7).

The example above sets the potentiometer wiper to mid-value: mcp4151.setWiper(128).
Generally the wiper can be set to values from 0 to 256.
The wiper is also known as pin P0W or pin 6 (look into your datasheet pinout picture).
If we compare the digital potentiometer to an analog potentiometer where the wiper can be adjusted from one side of a resistance slider to the other side. Then a wiper value of 0 in this code library means that the wiper/slider is near P0B, while a wiper/slider value of 256 means the wiper/slider is near P0A. This is remembered from my measurements - please make sure to verify yourself to be safe.
The included Arduino example sketch ./examples/UserPotentiometerValueInput accessible in Arduino IDE via

Files --> Examples --> MCP4151 --> UserPotentiometerValueInput

can be used to manually set values for the wiper and analyse potentiometer/voltage divider behavior.

Click here in Github on the green <>Code button and then Download ZIP.

<>Code --> Download ZIP (here in GitHub)

Then in the Arduino IDE click:

Sketch --> Include Library --> Add .ZIP Library...

And select the ZIP file you downloaded in the first step. The Arduino IDE then quickly will inform you about successful installation.
Then if you have a sketch that you want to use the library in go to the Arduino IDE menu bar and click:

Sketch --> Include Library --> MCP4151

and use the functionality of this library in your sketch. Happy coding!

Arduino Library Manager inclusion is coming soon.
Support for mutliple MCP4151 devices sharing the same SCK and SDIO pins on the Arduino are an idea.