The following compile command-line worked for me to statically link the mysql client libs:
gcc -I/usr/include/mysql -c mysql.c
gcc -o mysql mysql.o -static -lmysqlclient -static-libgcc -lm -lz -lpthread
However, I received the following warnings, which may or may not be a problem for you. It seems to be saying that there is a dependency on the target machine having the same glibc version as your build machine.
/usr/lib/gcc/i486-linux-gnu/4.2.4/../../../../lib/libmysqlclient.a(mf_pack.o): In function `unpack_dirname':
(.text+0x6cc): warning: Using 'getpwnam' in statically linked applications requires at runtime the shared libraries from the glibc version used for linking
/usr/lib/gcc/i486-linux-gnu/4.2.4/../../../../lib/libmysqlclient.a(libmysql.o): In function `read_user_name':
(.text+0x5ed7): warning: Using 'getpwuid' in statically linked applications requires at runtime the shared libraries from the glibc version used for linking
/usr/lib/gcc/i486-linux-gnu/4.2.4/../../../../lib/libmysqlclient.a(mf_pack.o): In function `unpack_dirname':
(.text+0x6e1): warning: Using 'endpwent' in statically linked applications requires at runtime the shared libraries from the glibc version used for linking
/usr/lib/gcc/i486-linux-gnu/4.2.4/../../../../lib/libmysqlclient.a(my_gethostbyname.o): In function `my_gethostbyname_r':
(.text+0x3c): warning: Using 'gethostbyname_r' in statically linked applications requires at runtime the shared libraries from the glibc version used for linking
/usr/lib/gcc/i486-linux-gnu/4.2.4/../../../../lib/libmysqlclient.a(libmysql.o): In function `mysql_server_init':
(.text+0x695d): warning: Using 'getservbyname' in statically linked applications requires at runtime the shared libraries from the glibc version used for linking