That fan, like any other, will require connection to two things. In fact, consider an ARGB Fan this way: it really is TWO devices in one unit: a fan (in this case, a 4-pin PWM type) and RGB lighting LED's in the frame. Each device has its own connection cable with a female connector in its end. Each cable needs to plug into a header that provides two functions: power is supplied, plus control of the device options (speed, or colour). You are familiar with the way that works for the fan motor part. Likewise, the ARGB connector on the end of the other cable needs such functions provided from somewhere. One option for that is to buy from Cooler Master their Addressable RGB LED Small Controller, a box that gets power from a SATA output from the PSU and has three buttons on it you can use to change the RGB lighting display manually.
But many mobos now have RGB headers built into them, and the control of lighting displays for devices plugged into such a header is done with a software utility that is supplied free by the mobo maker - no manual box with a connecting wire. HOWEVER, there are two INcompatible systems widely used for RGB lighting now. One is called just plain RGB and uses a 4-pin header that supplies a common +12 VDC power line and three separate Ground lines, one for each of the three RGB colours. The other is the more advanced Addressable RGB or ADDR RGB or ARGB system that uses a 3-pin header (very much like the 4-pin one, but missing one pin in the line) that contains common + 5 VDC and Ground lines and a Control Line. The way the LED's in the lighting device (strip or fan frame or whatever) are connected and controlled is different between these two systems, as well as the difference in power supply voltage, so you cannot mix them in one circuit.
So, OP, to power and control any RGB system from a mobo header using the mobo software to do the control, requires that your mobo have one of these headers on it, AND that you buy the RGB lighting device of the SAME TYPE as what your mobo has. In your case you would like to use the ARGB type of device, so you would need a mobo ARGB header to do it this way. If you do not have that on your mobo, then you do need some separate device to provide power and control. The simple manual box I mentioned is one way, and there are others.
To help, post back here the maker and exact model number of your mobo, and we can tell you what RGB capabilities it has, if any.