Is there a way to pick up Skeleton Arrows?

No. You cannot do this in the PC and console versions of the game either. As that answer states and the Wiki states:

Arrows originally shot by skeletons, strays, illusioners, pillagers, players in Creative, players using the Infinity enchantment, or duplicate arrows created by Crossbows with the Multishot enchantment cannot be collected.

With the exception of mods for the PC version, its not possible in any version of the game including Bedrock Edition. This is likely due to the fact that it would make it pretty easy to farm arrows form a skeleton.

No. Arrows shot by skeletons cannot be picked up by the player. Only arrows shot by the player (without the infinity enchantment) and missed can be picked up.