In my RC servo motor datasheet the shall current is 600 mA. My Arduino cannot supply that much of current so, I decided to use an DC adapter to supply the power and arduino to control the Servo. My question is - Can I connect a DC adapter of 5 volts and 1A to the servo. I have read some where that servo motor just take current (not voltage) what it needs even tough you supply more than enough. Is it right?
Yes, 5V 1A should be more than adequate for that servo.
Based on my own playing with with a Tower Hobbies Royal Titan, years ago, I suggest putting about a 250 uF capacitor across the servo supply, ideally as electrically close to the servo as you can. A servo can pull surprising current spikes.