Many modern compilers already perform automatic tail-recursion optimisations, and I suspect rustc does too.

According to cargo-asm, the following is your function in assembly. Despite my very shallow knowledge in assembly, I believe it is tail-recursion optimised since there are only jumps and no calls.

rust_test::zeros:
 je      .LBB0_1
 mov     r8, rcx
 xor     ecx, ecx
 movabs  r9, -3689348814741910323
.LBB0_3:
 mov     rax, r8
 mul     r9
 shr     rdx, 2
 add     rcx, rdx
 cmp     r8, 4
 mov     r8, rdx
 ja      .LBB0_3
 mov     rax, rcx
 ret
.LBB0_1:
 xor     ecx, ecx
 mov     rax, rcx
 ret