There are two mentions of Candy's being one-handed. The first one is described in Chapter 2 in the fourth paragraph (page 18 of the Penguin edition)--
He pointed with his right arm, and out of the sleeve came a round stick-like wrist, but no hand.
Then, in Chapter 3 in the third paragraph on page 60, Candy's loss of a hand is also mentioned--
He scratched the stump of his wrist nervously.
Because Candy lost his hand on the ranch, the boss compensated him with two hundred and fifty dollars and gave him the job of swamper. Nevertheless, Candy is always anxious about his position; for example, when he first enters the bunkhouse in which George and Lennie are talking, Candy is quick to assure them,
"I wasn't listenin' I was jus' standin' in the shade a minute scratchin' my dog. I jus' now finished swampin' out the wash house."
In another instance, after Candy tells George and Lennie about Curley, he asks them, "Don't tell Curley I said none of this. He'd slough [fire] me...."
Further, as he listens to George and Lennie discuss their dream of owning a place of their own one day, Candy becomes eager to be a part of this plan. He offers to contribute his savings and even promises to make a will that leaves his money to them. Scratching the "stump of his wrist nervously," Candy adds that he thinks he will be fired soon because of his age:
"Jus' as soon as I can't swamp out no bunk houses they'll put me on the county."
Candy's physical handicap becomes symbolic of the crippling state of all the dispossessed men who migrate from place to place in search of seasonal work with little hope of anything permanent in their lives.