In most areas of PA, yes you can. There are some cities (Philly proper, I believe, and Harrisburg maybe?) that don't allow home baking at all. Individual cities and boroughs have their own laws.
As far as the Ag Dept is concerned, you can license a rental home/apt kitchen.
BUT - you first need to get approval from your landlord. If the property owner doesn't want you to run a business from their property using their equipment (oven, fridge, sink, water pipes, etc etc), then you can't.
AND you need to seek approval from your city/town/borough first. They may not allow any sort of business run from a residence. Different boroughs have different rules about zoning. Get a written approval to operate a home business from the town - the Ag Dept will likely require this.
At that point you should go through the (simple) licensing process with the Ag Dept. They'll help guide you through any other things you'll need such as tax IDs and such. 
Contact your local county or board of health department. That would be a far better resource than here.
Another thing you have to consider is insurance. The landlord's insurance may not cover a separate business or allow it. Definitely check with your landlord as well as the health department.
I know in Illinois, you can't do it out of your home if you rent the house. Mainly because you would have to remodel another room in your home to have the whole seperate kitchen thing, and I'm sure most landlords would not go for that. I barely did cakes at all and only did them for family for about 5 years until we finally bought our house, and the county health inspector was the first person I called when we moved in so we could get started. I was legal in less than 3 months.
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