When my air conditioner cycles on, I notice my lights blink. Is this normal?

Yes this is completely normal for when most HVAC systems turn on. If your lights dim for less than a second or their brightness is reduced by only a fraction then it shouldn’t be a cause for concern as it has no negative effect on the electrical system. The cause for concern only comes if your lights flicker constantly when the system is on or noticeably brighten before flickering as this may indicate a larger issue at hand. The most common causes of continued light flickering are circuit overload, exposed wires, damaged wires, maxed out distribution panel, or a damaged/weak AC capacitor.