Can itchy breasts be a sign of breast cancer?

Not usually. Painless lump is the main sign of breast cancer. So look for any lump. Otherwise go see a skin specialist(dermatologist in case the itching is severe or getting worse...It may go away on its own if it is minor probelm.
Generally no. Breast cancer in its early stages has no symptoms. A firm breast lump can form over time. An uncommon form of breast cancer can present as a nipple scaling lesion, paget's. Pain or itching are not usually seen in breast cancer. But you should have an examination with your doctor to be sure.