Cut the carrots to a size that fits your juicer and begin juicing according to the user’s manual.Chop the carrots and run though the juicer: Leave them unpeeled if you’re using organic carrots – the skin contains concentrated vitamin C and niacin. You can peel them if you’re using conventional carrots – the concentration of pesticides is higher in the peel. How To Make Carrot Juice With A Juicer Step 1. The best carrot juice is made in a slow masticating juicer, it’s cold pressed (unless you use a centrifugal juicer) and not exposed to metal or heat (which contributes to oxidation).