The shell function.

You can use shell function: current_dir = $(shell pwd).
Or shell in combination with notdir, if you need not absolute path:
current_dir = $(notdir $(shell pwd)).

Update.

Given solution only works when you are running make from the Makefile’s current directory.
As @Flimm noted:

Note that this returns the current working directory, not the parent directory of the Makefile.
For example, if you run cd /; make -f /home/username/project/Makefile, the current_dir variable will be /, not /home/username/project/.

Code below will work for Makefiles invoked from any directory:

mkfile_path := $(abspath $(lastword $(MAKEFILE_LIST)))
current_dir := $(notdir $(patsubst %/,%,$(dir $(mkfile_path))))