AFAIK gcc doesn't provide such an option. The standard, as you cited, says:
N3690 - §5.8.3
The value of E1 >> E2 is E1 right-shifted E2 bit positions. If E1 has
an unsigned type or if E1 has a signed type and a non-negative value,
the value of the result is the integral part of the quotient of
E1/2E2. If E1 has a signed type and a negative value, the resulting
value is implementation-defined.
and that means doing
int si = -1;
int right = si >> 1;
might or might not yield -1 as a result. It's implementation defined. And that means the compiler is not forced to yield a warning like "other compilers might do this another way".
Some of the reasons for this choice follow.
The original K&R passage says:
"Right shifting an unsigned quantity, fills vacated bits with 0. Right
shifting a signed quantity will fill with sign bits (arithmetic shift)
on some machines such as the PDP-11, and with 0 bits (logical shift)
on others."
this means that the operation is architecture-dependent. The reason behind this is that some architectures are fast in doing one of the two but not both.
This reason plus the fact that the usefulness of sign-extended shifts is marginal made the standard take the choice of leaving it "implementation defined". By "usefulness of sign-extended shifts" I mean that right shifting a negative signed integer arithmetically does not work as the positive counterpart (because losing a 1 on the right makes the negative number smaller, i.e. bigger in modulus)
+63 >> 1 = +31 (integral part of quotient E1/2E2)
00111111 >> 1 = 00011111
-63 >> 1 = -32
11000001 >> 1 = 11100000
References for further reading:
https://mcmap.net/q/378950/-right-shifting-negative-numbers-in-c
http://www.ccsinfo.com/forum/viewtopic.php?t=45711
https://isocpp.org/std/the-standard
Edit: if the above doesn't address the issue (i.e. the code is valid, why should a compiler warn about that?) I'm providing a second solution: AST matchers
As described here: http://eli.thegreenplace.net/2014/07/29/ast-matchers-and-clang-refactoring-tools/ you can write some code to identify quickly all the right-shifts-with-signed-integers spots in your program.
Think of it as "writing my small one-task static analysis checker".
Edit 2: you might also try other static-analysis tools, clang has a -fsanitize=shift option which could work for you. AFAIK also for gcc they were implementing an undefined behavior sanitizer which could help diagnosing those errors. I've not been following the story but I guess you could give it a try as well.