Can I replace the charging port?

I see the tear down guide on ifixit, you can have a look and this can be your guide until you can see the charging port. Motorola Droid 4 Teardown

But if this part in green lines is charging port, i guess it may be soldered on the mother board, so it's not easy to replace it.

Actually the port circled in green is the HDMI video port, the USB charging port is the one next to it to the left. You may be able to improve the situation if you have a good, very small (not available at Radio Shack) soldering iron and a steady hand. Remove the rubber gasket that cover the two ports. Note the port is held down to the motherboard with 4 solder tabs at the sides, in addition to the microscopic connector pins in the middle. Inspect the 4 tabs with a bright light and a strong magnifier, you may note that one of more of the tabs has broken loose from the board. Resolder the tab(s) while using a spudger to press the jack tightly down against the MoBo. Be very careful, and good luck. If the pins have broken loose, you are probably SOL.