So Cronbach Alpha is a measure of internal consistency and it is typically used as a way to assess reliability. Cronbach is performed by adding a set of independent variables together (you can do it for a set of questions that constitute your dependent variable too) and then to calculate alpha which indicate greater agreement or lesser agreement.
You cannot look at Cronbach's alpha for 1 item. Hence all the items you include should be related to the same construct. Thus, if you have 15 items that specifically relate to anxiety then you can perform Cronbach's alpha once with all 15 items included. If you have smaller constructs within anxiety, you should group those and perform the analysis for specific sets. All of these considerations should be be based on the theoretical reasons you chose that specific set of questions/scale/inventory.
SPSS and I am sure R will have smiliar routines where you can add all the item and then you can also see which item lowered the overall reliability and in that way find an optimal set to enhance the internal consistency but once again caution should be applied in how this is performed and how item exclusion is done (i.e. did participants fail to read the question properly etc etc etc).