A proper shunt resistor will be made of manganin (or, less commonly, constantan) because these alloys have relatively high bulk resistivity and a near-zero temperature coefficient of resistance, but you can get decent results with stainless steel. The tempco of stainless steel isn't zero, but it's much lower than mild steel and doesn't corrode/rust.
For example, a 1mm diameter 316SS wire that is 10.61cm long will have a resistance of 0.100 Ohms (bulk resistivity of 74 microOhms-cm).