Question
Our cat broke a few branches from a new English Oak tree we planted.  Can we root the branches?

Also,  can acorns be used to start a new oak tree?

Answer
Oak species are propagated by seed. The acorns are planted as soon as they mature and left outside over the winter. Named cultivars are propagated by grafting. Fast growing sucker shoots (sometimes called "water sprouts") are grafted onto seedlings of the same or a related species.
Cuttings will root very poorly and in the vast majority of the time will not root at all. Best to use acorns.

Choose swollen or plump-looking, mature acorns from healthy trees and pick them off the ground as soon as possible. Whites start sprouting soon after they fall--even if it has started its shoot, you can still collect it.

Put acorns in a plastic bag with an equal amount of leaf mold or peat mix and barley dampen. Close the bag loosely and store in the refrigerator at between 32 to 35 degrees (whites will continue to sprout at between 36 and 39 degrees). Check acorns throughout the winter and keep just barely damp. Acorns need about 1000 hours of low temperature dormancy. Plan to plant your acorns in late April from the 15th to the 20th. You can leave them in the refrigerator and plant as late as July, but an early start will produce stronger seedlings.

Do not use garden dirt since it packs and may carry diseases. Use a good quality potting soil mixed with the same amount of milled sphangnum moss. You want a porous, sponge-like soil. Take an 8 ounce styrofoam cup and punch three to four pencil-sized holes in the sides next to the bottom. Fill to the top and tap to settle the soil leaving about an inch watering space. Place the acorn horizontally, barely under the surface. Water until it comes out the bottom and place cups on a southern windowsill. Never let the soil get completely dry, always prime first and water until it drains. Check moisture daily or more often if necessary.

In about three weeks the stalk will be five to six inches and the first set of leaves will have spread. About mid-May it is time to harden the plants off. Gradually increase exposure time to outside sun and air. Set the trees outside during the day and return them to house or garage at night.

Around late May you can transplant to a 16 ounce cup. Check to see if roots are curling around the bottom of the 8 ounce cups.

Remember to punch drain holes and use a mix of half potting soil and half leaf mold from the forest floor or leaf compost. Settle the mix by tapping again and leave one inch watering space after transplanting the seedling. Now your trees can be kept outside all the time, but be sure to check them for drying out in sun and wind. Keep them damp.

With the second flush of leaves your seedlings can be transplanted into a 32 ounce, tall, food container. Check the taproot and see if it is bending around the bottom of the cup before transplanting. White and healthy-looking roots are a sign of vigor. Use the same soil mix and provide drain holes. The larger container will hold moisture longer but be sure to check it regularly.

Once they reach about 10-12 inches tall they can be transplanted to where you want them to grow.