To run make from the command line using Intel® C++ Compiler, make sure that /usr/bin is in your path.
To use the Intel compiler, your makefile must include the setting CC=icc. Use the same setting on the command line to instruct the makefile to use the Intel compiler. If your makefile is written for gcc, the GNU* C compiler, you will need to change those command line options not recognized by the Intel compiler. Then you can compile:
make -f my_makefile