Your car's battery should be marked with a CCA (cold cranking amps) rating. If its the correct battery for your car model, that will give you some idea of the max current you are likely to see.
Provided the vehicle has rubber tires (i.e. not a boat or tracked vehicle) yoou could insert a suitable current shunt (probably 500A or 1000A) in series with the battery negative lead, and scope the voltage across it with a DSO, one-shot triggering on the switched supply voltage to the starter solonoid. The *ONLY* ground to the vehicle chassis should be via the scope ground clip, which is why it must be on rubber tires. If its not on rubber tyres, you'd need to use a handheld scope or one with isolated inputs. The current shunt will typically have 50mV, 75mV or 100mV across it at its max rated current - see its specifications for details.