It will depend on the Wattage of your Power Supply. How many watts is the power supply you have in the PC now? Yes the card can work in your PC but if the power supply is to weak you will need to change it out for a more powerful one.
EDIT: found this on your PC. http://reviews.cnet.com/desktops/acer-aspire-m3470-uc30p/4507-3118_7-35607573.html
According to this your PSU is a 300W. You will need to change the Power Supply for that card to work in your PC.