Acidic or not?

Although $AlCl_{3}$ is covalent when anhydrous but it becomes ionic in aqueous solution.

In aqueous medium $Al^{+3}$ exists as a complex $[Al(H_{2}O)_{6}]^{+3}$ .

This complex contains $Al — O$ bond, which is very strong bond and it weakens $O—H$ bond. This is responsible for acidic character of the given solution.

$[Al(H_{2}O)_{6}]^{+3} \rightleftharpoons [Al(H_{2}O)_{5}OH]^{+2} + H^{+}$

There are two types of acids and bases; Bronsted-Lowry acids and bases and Lewis acids and Lewis bases.

A Bronsted-Lowry acid is a proton donor while a Bronsted-Lowry base is a proton acceptor. A Lewis acid is a substance that can accept a pair of electrons while a Lewis base is a substance that can donate a pair of electrons. If one were to observe Bronsted Lowry acid-base reactions theoretically, one would observe that Bronsted Lowry acids and bases is a subset of Lewis acids and bases.

As can be seen in the image, aluminium trichloride can accept a pair of electrons, so it is acidic.