More questions than answers, but the answer should emerge as you answer these questions:
MCP4922 datasheet here.
Please provide complete circuit diagram of what you are ACTUALLY doing?
Try feeding DAC Vdd also from Vref.
Note that DAC Vdd needs to be such that SPI signals provide valid high and low logical levels at both ends of SPI link. This MAY be able to be accomplished when Vdd_sender <> Vdd_DAC but it is usually better if they are the same.
What is load on each DAC output?
What voltage is "my power rail"?
What voltage is DAC Vdd?
What current can your Ref supply?
NB: as it is a shunt regulator its current feed capability at 5V depends critically on its feed resistor.
Is ground connected correctly in all cases?
ADDED
This is ambiguous:
- ... (DAC) vdd should be the same voltage as my arduino They both run at 5v. The psu rail is also at 5v. Its can supply upto 10ma. It's the same one I post posted about earlier on (LM336). However I didnt have the resistor size you suggested so I reapplied ohms law and came up with 8.2k. According to my dodgy math it's 1ma current.
The circuit diagram that you posted is what you are APPROXIMATELY trying to copy.
You have changed a number of things.
You are using words like 'power supply', "It can supply", "psu rail" etc but it is unclear what reference is to which device and what connections are really made. I could probably have a reasonably good guess at what you mean and what you think you are doing BUT I may get it wrong and YOU may have got it wrong. If you post a diagram of EXACTLY what you think you hav done then we can tell you what you should see and we can go from there. As is there are too many uncertainties. You need to show Arduino as a block diagram, basic Arduino powering with voltages, SPI connections, ALL DAC power and signal connections and regulators and resistors and connections. In you other post you mention a 12V supply - is this still supplying the Vref regulator. Don't just tell me - show it on your diagram. A hand drawn diagram is fine as long as it is clear, well labelled and unambiguous. It need only include the circuitry relevant to the question, but more is OK.
165k input impedance is NOT a problem. This just shows that the DAC load is light compared to drive capability or other loads, which is good.