Odysseus gave his wine to the Cyclops because he wanted to trick the Cyclops by getting him drunk and weakening him.
Cyclops captured Odysseus and his men in his cave and treated them in the most inhospitable manner. To come out from his captivity, Odysseus makes a strategy. He makes his drink very strong and offers it to Cyclops. After consuming the drink, Cyclops passes out. With the help of a burning piece of wood, Odysseus blinds Cyclops. This was the escape plan of Odysseus in order to run out of his cave.