It was announced last year that the Mojang accounts of Minecraft Java Edition players will be migrated over to Microsoft accounts. This transition has already begun, and although it may be slightly inconvenient, Java Edition players who make the migration will be awarded their very own capes.

These capes are said to be slowly rolled out into player's accounts starting mid-July, so hopefully the perk starts to show up soon. After the initial roll out, any Java Edition player who makes the transition to Microsoft after that should automatically receive the cape.
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Thankfully, there are plenty of online mods available that allow players to add capes to their look. They will simply need to pick which mod offers their most ideal cape style and then install it into Minecraft.

However, it should be noted that only players with the same particular mod pack installed will be able to see the cape in action.

This could be useful for those playing on SMPs with friends if everyone is able to download the same mod. Or, the addition of a cape via mod packs can simply be for a player's own benefit and enjoyment.

Skins

Unfortunately, for Minecraft Java Edition, there are no skins that will automatically incorporate a cape. However, in Bedrock Edition, there are some skin packs that come with capes included.