SSIS convert DT_WSTR to date
You have to use convert DT_WSTR to DT_DBTIMESTAMP. You can find BOL reference here.

for e.g.instead of "Getdate()" use your Date_Column 

(DB_TIMESTAMP)((DT_WSTR,4)YEAR(GETDATE()) + RIGHT("0" + (DT_WSTR,2)MONTH(GETDATE()),2) + RIGHT("0" + (DT_WSTR,2)DAY(GETDATE()),2) + (DT_WSTR,10) Time_Column)


Also,  you can use the Data Conversion transformation, which is probably easier if you are only changing the data type.

EDIT: You can also look for an option of SSIS GoogleAnalyticsSource from codeplex.