Hi @canblue ,
The power jack charging port is a plug in module so it should be easy to replace it.
Here is a link to the ifixit [guide|78473] guide. It is useful as it shows how to get access to the motherboard in the laptop, so that the charging port can be replaced.
Here is a [https://www.youtube.com/watch?v=hlSn0Mj6D6Y|video] which may also be of some help. Not the same model number but close enough to be of some use.
Here is a link to just one [http://www.nbjack.com/acer-aspire-e1572-e1572g-e1572p-power-jack-charging-port-dc-in-cable-harness-p-2098.html|supplier]. It is not a recommendation to use them it is shown to give an idea of the cost of the part. There are others online that may suit you better. Just search for ''Acer Aspire E1-572-6676 Dc-In jack part'' to get results. The part is the same for all Acer Aspire E1-572, E1-572G and E1-572P Series laptops
Hopefully this is of some help