Let $𝕋$ be a periodic time scale. The purpose of this paper is to use a modification of Krasnoselskii’s fixed point theorem due to Burton to prove the existence of periodic solutions on time scale of the nonlinear dynamic equation with variable delay $x^{▵}\left(t\right)=-a\left(t\right)h\left(x^{\sigma }\left(t\right)\right)+c\left(t\right)x^{\widetilde{▵}}\left(t-r\left(t\right)\right)+G\left(t,x\left(t\right),x\left(t-r\left(t\right)\right)\right)$, $t\in 𝕋$, where $f^{▵}$ is the $▵$-derivative on $𝕋$ and $f^{\widetilde{▵}}$ is the $▵$-derivative on $(id-r)\left(𝕋\right)$. We invert the given equation to obtain an equivalent integral equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show...