Yes, something like this:

  static inline long read(int fd, void *buf, long count) {
    register long rax asm("rax") = __NR_read;
    register long rdi asm("rdi") = (long)fd;
    register long rsi asm("rsi") = (long)buf;
    register long rdx asm("rdx") = count;

    asm volatile(
        "syscall"
        : "+r"(rax)
        : "r"(rdi), "r"(rsi), "r"(rdx)
        : "rcx", "r11", "memory"
    );
    return rax;
  }

The linux kernel also has its own headers (IIRC it was something like <asm/unistd.h> and/or <sys/syscall.h>, but might depend on architecture and version) where it will provide the stub asm statements.

In my memory the syscall ABI has changed a few times (i386 had int $0x80, then sysenter, then abstracting it in the vdso, then amd64 has 'syscall'), so it may be easier to let the kernel header provide the mechanism.