Which among the following salts turns blue litmus red in its aqueous solution?

To identify the salt that yields an acidic aqueous solution—thus turning blue litmus red—consider the hydrolysis behavior based on the strength of the parent acid and base.

Option A, $\text{KCN}$, derives from a strong base (KOH) and weak acid (HCN). The cyanide ion hydrolyzes as $\text{CN}^- + \text{H}_2\text{O} \rightleftharpoons \text{HCN} + \text{OH}^-$, producing hydroxide ions and resulting in a basic solution.

Option B, $\text{Na}_2\text{CO}_3$, originates from a strong base (NaOH) and weak acid ($\text{H}_2\text{CO}_3$). The carbonate ion hydrolyzes via $\text{CO}_3^{2-} + \text{H}_2\text{O} \rightleftharpoons \text{HCO}_3^- + \text{OH}^-$, also yielding a basic solution.

Option C, $\text{NaNO}_3$, is formed from a strong base (NaOH) and strong acid ($\text{HNO}_3$). Neither ion hydrolyzes significantly, so the solution remains neutral.

Option D, $\text{CuCl}_2$, arises from a weak base ($\text{Cu(OH)}_2$) and strong acid (HCl). The copper(II) ion hydrolyzes as $\text{Cu}^{2+} + 2\text{H}_2\text{O} \rightleftharpoons \text{Cu(OH)}_2 + 2\text{H}^+$, producing hydrogen ions and creating an acidic solution.

Consequently, $\text{CuCl}_2$ is the salt that turns blue litmus red.

The final answer is $\boxed{\text{D}}$