Change your code with
byte[] dataBytes = stringToSign.getBytes();
PKCS1SignatureSigner signer = new PKCS1SignatureSigner(rsaKeyPair.getRSAPrivateKey());
signer.update(dataBytes, 0, dataBytes.length);
byte[] signatureBytes = new byte[signer.getLength()];
signer.sign(signatureBytes, 0);
String signedIdentifier = Base64.encode(signatureBytes);