Large pretrained language models (LLMs) have shown surprising In-Context Learning (ICL) ability. An important application in deploying large language models is to augment LLMs with a private database for some specific task. The main problem with this promising commercial use is that LLMs have been shown to memorize their training data and their prompt data are vulnerable to membership inference attacks (MIA) and prompt leaking attacks. In order to deal with this problem, we treat LLMs as untrusted in privacy and propose a locally differentially private framework of in-context learning(LDP-ICL) in the settings where labels are sensitive. Considering the mechanisms of in-context learning in Transformers by gradient descent, we provide an analysis of the trade-off between privacy and utility in such LDP-ICL for classification. Moreover, we apply LDP-ICL to the discrete distribution estimation problem. In the end, we perform several experiments to demonstrate our analysis results.