If your current power supply can run a 6850 no problem then it can handle a 7870 no problem. If it were me I would upgrade the PSU anyway because its the most important part in your case and you want it to be top quality.
If on a tight budget just go for the GPU, if you can swing it, pick up something like this.
SeaSonic M12II 520 Bronze 520W - $70http://www.newegg.com/Product/Product.aspx?Item=N82E16817151093
SAPPHIRE 100354OCL Radeon HD 7870 GHz Edition 2GB - $240http://www.newegg.com/Product/Product.aspx?Item=N82E16814202010
But like I said you have enough power to run a 7870 but I would put a higher quality unit in there just to be sure.