Single supply non-inverting amplifier using op amp
Your schematic should be as following:







simulate this circuit &ndash; Schematic created using CircuitLab

Since you're using a single-supply non-inverting amplifier, the non-inv input of the opamp should be biased to a non-zero voltage –ideally to Vcc/2 as in your schematic so that the amplified signal can swing equally.

Now let's take a look at the capacitors in dashed rectangles:


If you don't put C2, the DC bias will be multiplied by 11 as well. Thus the output will saturate and you'll never get the amplified signal from output. Since C2 will be open in DC, the net gain in DC will be unity. Thus the DC bias will be multiplied by 1. So the amplified signal will have an offset of Vcc/2 instead of 11 x Vcc/2.
C3 is just a DC-blocking capacitor. It removes the DC offset so you can get only the amplified AC signal.