controlling esc with an arduino

I'm trying to use an arduino to control an esc this one

is there anyway I can control the speed with the arduino

Looks like a RC speedcontroller. If that is the case, it's just another servo to your Arduino. So connect it like it is a servo and play a bit around to find the correct values. I see a remark BEC mentioned. I think that means it can eliminate the use of a separate battery for the RC receiver. Be sure to connect it correctly so you don't damage your Arduino. The 3 wire (black, red, white) are GND, 5 volt and a PWM pin.

In other words use the Servo library. All ESCs have arming sequences at start up, which often means holding the throttle at minimum for a couple of seconds (RC controls park at mid-point, so requiring minimum throttle means the operator has to deliberately hold the throttle back to arm the ESC). This equates to something like

Servo servo ;

void setup ()
  servo.attach (servopin) ;
  servo.write (0) ;
  delay (2000) ;

[ untested code ]

but ESCs do vary.

Previous ESC related post.