What is JotForm?
JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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We believe that if one user has a question, there could be more users who may have the same question. This is why many of our support forum threads are public and available to be searched and viewed. If you’d like help immediately, feel free to search for a similar question, or submit your question or concern.
You cannot do this in the DateTime field within the form builder. You can do it if you used the form's full source code and just modify the DateTime field in the source code.
Or you can use Calculation to concatenate Month and Year field to have Month/Year data.
Create first the 2 fields (Month and Year) using drop-down field.
There is a special value option for drop-down field that you can use already for the Year data(the "Last 100 Years" option). For the Months, simply use 1-12 numbers.
Sample form http://www.jotform.me/form/42448558863468
Hope this help. Inform us if there is more we can assist you with.