It is possible to do this, but very difficult, generally recommended against, and almost certainly unnecessary.
What you've asked is how to install the Debian package management system on a Red Hat system.
The package management system tracks what packages are installed in a system, facilitating installation and updates of packages, tracking dependencies, and avoiding conflicts between packages. Particularly for the latter two reasons, different package management systems are fundamentally incompatible with each other; trying to use two different systems simultaneously will, without very careful supervision, quickly render your system unusable, because you would effectively be trying to install two different Linux distributions on top of each other.
When one maps the family tree of Linux distributions, the primary branching point is the choice of package management system. The two most common systems are the Debian package management system, DPKG, and the Red Hat Package Management system, RPM. "apt-get" is a front-end for using the DPKG system, and it requires the rest of the toolset to work; likewise, "yum" is a front-end for using the RPM system.
It is sometimes possible to convert a package from one system to the other. alien is an application for doing this. Note that it's almost never mentioned without warning that it isn't reliable.
If the problem you want to solve is that you want to install a specific application on a Red Hat system, then you may find it works better to use a package from another Linux distribution that uses RPM; rpmfind can help you search. It's slightly more reliable to find a source RPM and rebuild it on your system; that reduces the likelihood of problems with dependencies on specific compiled binaries. Or, you can bypass package management by finding the source tarball for the application and compiling it.
If the problem you want to solve is having more packages available in general, then you should bear in mind that Red Hat Enterprise Linux, by design, has an emphasis on stability, and its official repositories are relatively limited. You may prefer using the closely related Fedora Linux, which has a far larger selection of packages in its official repositories, or you may want to switch to Debian or one of its derivatives.