What is the maximum frequency at which Arduino Due can sample a real signal ?

i need to acquire injector signals ( 4 injectors at same time) at the rate of 1 microsec
and process it and transfer the processed / integrated data via CAN shield.

Can this be done via arduino due board , Is it possible?

No. You can sample 1 input at 1MHz, 4 inputs at 250 kHz.

Thanks Magician

Okey how could is sample 1 signal at 1 MHZ ...

I tried using analogread() function and output a pulse wave form in pin 13 ,

what i see is after 2khz the information from input signal seems to be missing ....

What kind of "processing" are you gonna to do?
From SAM3x data sheet:

The CAN controller provides all the features required to implement the serial communication
protocol CAN defined by Robert Bosch GmbH, the CAN specification as referred to by
ISO/11898A (2.0 Part A and 2.0 Part B) for high speeds and ISO/11519-2 for low speeds. The
CAN Controller is able to handle all types of frames (Data, Remote, Error and Overload) and
achieves a bitrate of 1 Mbit/sec.

It means you 'll have to reduce a data rate from 12 Mbits down to 1 Mb/s. I'd be cautious, and check if uCPU 'd be able to compress data at such high rate.

Regarding sampling, get code from this link, sampling configuration part 'll run w/o fft library.
Maximum sampling rate about 960 ksps, if you need exactly 1 Msps, than some tweaks necessary to set ADC in free running mode - the only mode capable to get you 1 Msps.