What the minimum current input that must be provided to Pi's GPIO input in order to get high value?
The idea: I will be adding Microwave Doppler which output are in micro amperes. I want to know if it will be able to read high input into pin.
This answer provides some insight in the electrical characteristics. The input current however is something nobody usually cares about as in digital circuits we usually assume low impedance outputs and high impedance inputs. That's fairly save to assume unless one considers "strange" logic families like ECL (a current-steering logic). That however is not relevant to the Pi.
GPIO Electrical Specifications (from Milliways' answer linked above) tries to give some estimates based on similar ARM based chips. Especially the Freescale MCIMX31 multimedia application processor (Table 15) lists a maximum input current for a high impedance input gate without pull-up/pull-down resistors of 1 microamp.
While this is just an estimate of a "similar" chip and the real Pi's SoC might be orders of magnitude different, it at least shows that there might be an issue down that road when connecting that particular source to a GPIO pin. Proper buffering with an additional external high impedance opamp, i.e. see here, seems to be the save way to go.