Yes We can connect MYSQL Database through C program.
MySQL database does support C program API just like PHP or perl.
The C API code is distributed with MySQL. It is included in the mysqlclient library and allows C programs to access a database.
Many of the clients in the MySQL source distribution are written in C. If you are looking for examples that demonstrate how to use the C API, take a look at these clients. You can find these in the clients directory in the MySQL source distribution.
Make sure you have development environment installed such as gcc, mysql development package etc. Following is the list summarize the list of packages to compile program:
mysql: MySQL client programs and shared library
mysqlclient: Backlevel MySQL shared libraries (old libs)
mysql-devel: Files for development of MySQL applications (a must have)
mysql-server: Mysql server itself
gcc, make and other development libs: GNU C compiler