Yes, this Blender supports this feature, which is frequently used on render-farms.
For reference, in Blender this is known as background mode.
I've had success rendering on a Linux cluster using SGE. Here, I render the first 1500 frames of an animation:
$ for n in `seq 1 1500`; do qbatch blender --background myblend.blend -x 1 -f $n; done
qbatch is just a script that submits a regular command line invocation to SGE for distribution to a compute node, so it's the stuff between "qbatch" and "done" that you're probably interested in)
Depending on the dynamics of your system, you may want to batch your renders differently, but you can adapt what I used.
Here is a page that describes some useful command line options: https://docs.blender.org/manual/en/dev/advanced/command_line/render.html