Help with BJT Transistor analysis. The amplified waveform is more like a square wave any needs to be more sinusoidal
The current through the base-emitter junction of a transistor is governed by the diode equation: \$i_e = I_S \left(e^\frac{v_{be}}{n\ V_T} - 1\right)\$.  At room temperature, \$V_T \simeq 26\mathrm{mV}\$.  So unless your peak-peak input voltage is significantly smaller than \$26\mathrm{mV}\$, you'll get distortion.

On the bright side, you have lots of excess gain in that circuit.  The quickest way to get more linearity is to put a resistor in series with the emitter, between the emitter and the intersection of R4 and C2.  I think I'd start with a value somewhere between \$200\Omega\$ and \$1000\Omega\$ and see how things look.

And -- don't think for a second that your resistor values are realistic.  1% resistors are standard these days, yet still a bit absurd for a transistor stage like that because any real transistor that you plug in there will add far more variation than a 5% resistor will.