Pour tangerine juice through a fine mesh sieve into a large bowl. Use a rubber spatula to press as much juice as you can through the sieve, discard remaining pulp. Add lemon juice, sugar, and corn syrup to the bowl. Stir with a spoon until the sugar has completely dissolved. Process in an ice cream maker according to manufacturer's instructions.
Serve immediately, or chill for a few hours. Best eaten the day it's made.
