You can very simply determine the amount of iron oxide by the change in mass:

It is necessary to weigh the glass vessel with iron on an accurate scale before pouring water, and after the corrosion test, carefully drain the water and calcine the vessel with iron at 100-120° until completely dry and weigh it again. The difference in masses before and after corrosion will be the mass of oxygen in the formed oxide of iron (Fe2O3). The mass of the oxide can be recalculated from this mass of oxygen by multiplying it by 3,333. You can also recalculate the mass of corroded iron by multiplying the mass of oxygen by 2,333.

With a hydrometer and a scale.

With that, you can determine the water density and know the theoretical mass considering the volume of the hydrometer jar, and at the same time, measure the liquid of the jar on the scale.

Of course, this will only work if the solution is not very concentrated in iron oxide.

To Vadim Verlotski , I would add the risk of having non-stoichiometric oxides, One can try with complexometric titration upon dissolving all the rust but not the metal (e.g. oxalic acid in anoxic environment), before which one needs to occlude oxygen from the vessel. Or simply, take out the rusterd piece and lightly brush or rinse with distilled water it to get rid of loose rust (and return the lossened rust to sollution), dissolve all rust etc in the solution with acid and titrate!