I am a us-residant here for last 6 years.I got 3rd degree felony charges (grand larceny $3000).I have court appearances on 23rd dec
I just wanted to know,can I apply for citizenship right now.

You can but the charges will still be there and any conviction on the records before any decission is made,

You are not going to get it though before the conviction. I would spend my time and money on attorneys to try and get the charges reduced

No, you must complete the whole process and wait for 3-5 years to prove that you are no longer involve in criminal activities, etc. Have immigration attorney handle your case when you are ready to apply for naturalization.