Yes, you can, although your statement of purpose and employment or work experience must detail why you want to go to a masters in applied cognitive psychology.  Typically, a masters degree is either a terminal degree (for employment) or a stepping stone to a doctoral (further research). You have to decide which road you want to take. They are different.

I would recommend that you take some college courses, even if they don't lead to a degree to show your interest in psychology. These courses could include general psychology, statistics in psychology and any courses in learning.

There are not many college programs that specifically cater to masters-level work in cognitive psychology. Most are part of learning or experimental psychology. One such masters in applied psychology is the University of Houston, Clear Lake. (https://www.uhcl.edu/documents/applied-cog-packet.pdf)

Masters in Psychology programs are relatively easy to get admitted to even if you don't have a BA in psychology. Your best bet it to apply to a wide range of MA programs as long as "BA in psychology" is not one of their requirements. I am not sure which exact colleges will accept you - you just need to check the MA admission requirements on the websites of all the top colleges.