yes you should be able to run a gtx 1070ti.
a hardware configuration basically never restricts a videocard (apart from bottlenecks)
Only real thing to consider is usually the power supply.
But the reccomended psu for a setup like yours is 500 watt.
But before you go out and get the graphics card, get a new psu aswell, the one you have might be 500 watts, but it seems like a very cheap grey psu.
i highly reccomend geting a new one, because i wouldn't trust such a cheap grey psu near my precious components.
As for psu reccomendations @LukeSavenije can probably give you the tier list.