If you need to move the angle of the charger to make it work you could have either a charger cord that is going bad, or a bad port.
The cord is the easier of the two to replace.
To check if it is the cord, try using a different cord on your phone and see if the problem persists. If it doesn't, then you just need to replace your phones cord. If it isn't the cord, you then need to check the port. Try using, again, a different cord to charge it. If it needs to be maneuvered around as before, even with the different cord, then your port is probably needing replacement. That 'usually' requires that the motherboard be replaced, as the port will be attached to the motherboard.
If you feel comfortable doing the work yourself, you can find loads of how to videos online. If not, then I am sure a local tech/repair shop could do it for you.