Yes, It is free to use. You may install and use it without any worries
Please see extract from link: Oracle Database Editions
Oracle Database Express Edition (Oracle Database XE) is an entry-level edition of Oracle Database that is quick to download, simple to install and manage, and is free to develop, deploy, and distribute. Oracle Database XE makes it easy to upgrade to the other editions of Oracle without costly and complex migrations. Oracle Database XE can be installed on any size machine with any number of CPUs, stores up to 4GB of user data, using up to 1GB of memory, and using only one CPU on the host machine. Support is provided by an online forum.
Hope this helps!