Yes, iOS 13 can be jailbroken. However, the process is not as simple as it was in previous versions of iOS. In order to jailbreak your iPhone or iPad running iOS 13, you will need to use a special jailbreak tool such as checkra1n or unc0ver.
Once you have jailbroken your device, you will be able to install third-party applications and tweaks that are not available through the App Store. You will also be able to customize your device to a greater extent than is possible with a non-jailbroken device.
However, it should be noted that jailbreaking comes with some risks. It could void your warranty and may make your device more vulnerable to security threats. Therefore, it is important to weigh the pros and cons before deciding whether or not to jailbreak your iOS 13 device.