To socialize a shy pet rat, you can start by spending quiet, quality time with them in a calm environment. Speak softly to your rat and offer them treats to help build trust. Gradually introduce handling by letting them sniff your hand and then gently pick them up. Provide plenty of opportunities for interaction through playtime and gentle handling to help your rat become more comfortable and sociable. Be patient and consistent in your efforts to help your shy pet rat feel more at ease around you.