let $x$ be a perfectoid space with tilt $x^\flat$. we build a natural map $\theta:\mathrm{pic} x^\flat\to\lim\mathrm{pic} x$ where the (inverse) limit is taken over the $p$-power map, and show that $\theta$ is an isomorphism if $r = \gamma(x,\mathcal{o}_x)$ is a perfectoid ring. as a consequence we obtain a characterization of when the picard groups of $x$ and $x^\flat$ agree in terms of the $p$-divisibility of $\mathrm{pic} x$. the main technical ingredient is the vanishing of higher derived limits of the unit group $r^*$, whence the main result follows from the grothendieck spectral sequence.