if (fork() == 0)
{
    // child
    int fd = open(file, O_RDWR | O_CREAT, S_IRUSR | S_IWUSR);

    dup2(fd, 1);   // make stdout go to file
    dup2(fd, 2);   // make stderr go to file - you may choose to not do this
                   // or perhaps send stderr to another file

    close(fd);     // fd no longer needed - the dup'ed handles are sufficient

    exec(...);
}