Identity theft can affect your credit score in a number of ways. First, the identity thieves can make inflated purchases in your name and this may leave you with very high bills which you may not be able to pay. Inability to pay bills usually leads to one having a low credit score.
Secondly, identity thieves can conceal all the transactions they have made using your credit card. You will therefore not be aware of the transactions and the deadline for repaying the bills may pass with the bills still unpaid. High and unpaid bills lead to a low credit score.
Thirdly, identity thieves can use your credit card information to open accounts in your name and then make transactions from these accounts. The bills from these accounts will be charged on you and since you may not be aware of them or you may be unable to pay them due to financial limitations, your credit score will go down.
Lastly, identity thieves can use the credit card information to withdraw all the money from your account. This may leave you financially dented and unable to pay your bills. Inability to pay your bills in turn leads to you having a low credit score.