Dear Dessalegn,

Cronbach's alpha works with scale and ordinal variables, not nominal variables. You may be able to turn nominal variables into multiple "dummy" binary variables but don't code the last one in order to avoid dependence.

However, a better approach for a single scale reliability analysis is to start with a Principal Component Analysis - see my advice sheet: https://www.researchgate.net/publication/280936182_Advice_on_Reliability_Analysis_with_Small_Samples

Technical Report Advice on Reliability Analysis with Small Samples

Both Cronbach's alpha and Principal Components Ananysis are based on correlations among the items, so they require at least ordinal data. They are not appropriate with nominal or multiple response data.

Desselgan, as both the learnd fellows said, Cronbach's alpha is used for ordinal or scaled data. It may not be fruitful for categorical data.

Peter,  if I may ask, for what purpose a nominal variable be tured to dummy variable? This is something new for me, however,  I am dealing with nominal data so your guidance may allow me find something related to my work. Thanks 

Reliability is relevant if the items are supposed to record a single underlying concept. It is not necessary for any collection of items given together in a given survey. In other words, reliability is meant for scales, not questionnaires. For a preliminary study with several categorical variables multiple correspondence analysis can be used for dimension reduction and visualization, and can be interpreted similarly to PCA. If, as others mentioned, you construct dummy (binary) variables from multiple-choice response format items perhaps you can use some model based on logistic regression, and even calculate some form of reliability, but I hesitate to say more without knowing details about your questionnaire.