Is there an easy way to test for the amount of iron (Fe) in water?
In a rainwater tank in contact with air, dissolved iron is probably oxidized to iron(III) ($\ce{Fe^3+}$).

A simple and sensitive test for $\ce{Fe^3+}$ in water uses thiocyanate ions ($\ce{SCN-}$, also known as rhodanide), which form the blood-red coloured complexes $\ce{[Fe(SCN)(H2O)5]^2+}$, $\ce{[Fe(SCN)2(H2O)4]+}$, and $\ce{[Fe(SCN)3(H2O)3]}$.

$$\ce{[Fe(H2O)6]^3+ + SCN- &lt;=&gt; [Fe(SCN)(H2O)5]^2+ + H2O}$$

Take a precise volume of the water (e.g. $10\ \mathrm{ml}$), acidify with dilute sulfuric acid (e.g. $2\ \mathrm{ml}$), add a thiocyanate solution (e.g. $5\ \mathrm{ml}$ $\ce{KSCN}$ or $\ce{NH4SCN}$, $c =0.5{–}2\ \mathrm{mol/l}$), and fill up with distilled water to a precise volume (e.g. $25\ \mathrm{ml}$).

An orange to red colour should appear.

The colour of the solution can be compared to that of standard solutions that contain known concentrations of $\ce{Fe^3+}$, e.g. prepared from iron(III) nitrate ($\ce{Fe(NO3)3.9H2O}$).

In a laboratory, the intensity of the red colour could be measured using a photometer.

Similar simple test kits are commercially available, e.g. for aquariums, garden ponds, or other water or soil samples.