I wonder if it's possible to access to the SIM card with an Android Application
You can get the IMEI like this (but is it what you want ?), just an exemple :
mTelephonyMgr = (TelephonyManager)getSystemService(Context.TELEPHONY_SERVICE);
String imei = mTelephonyMgr.getDeviceId();
Likewise, you have
String getSimCountryIso() : Returns the ISO country code equivalent for the SIM provider's country code.
String getSimOperator() : Returns the MCC+MNC (mobile country code + mobile network code) of the provider of the SIM.
String getSimOperatorName() : Returns the Service Provider Name (SPN).
String getSimSerialNumber() : Returns the serial number of the SIM, if applicable.
int getSimState() : Returns a constant indicating the state of the device SIM card.
String getSubscriberId() : Returns the unique subscriber ID, for example, the IMSI for a GSM phone.
For more, take a look at this page
and don't forget to add the correct permission in the manifest (getDeviceId() => Requires Permission: READ_PHONE_STATE)