Either one would be OK, and this is because “email” is something that can be thought of in different ways. Let me explain…
Think of "through" as sending something from one end to the other end of something that is continuous. Examples: The path goes through the forest (from one end to the other, with forest all around). The water runs into the house through the pipes. Blood runs through your veins.
Think of "via" as sending something using a service, or by means of a service. Examples: We sent the letter via messenger. (A messenger could be a person who picks up important documents by hand, bikes across the city, and delivers it by hand to the recipient. So “via messenger” is using the messenger service.) They repaired his stomach via surgery. (The service of surgery was used to heal his stomach.)
Since email is though of my people as both a service that routes messages, and also as a system of wires going through the houses and connecting up the world, it would be OK to use either phrase. Each one has a slightly different meaning.
I will send it through email means it will go through the wires of email to get to you.
I will send it via email means you’ll use the email service to deliver it.
But the first poster is correct, that it’s more common to say “by” in this case. “Via” is rarely used in spoken or informal language.
So I’d say “I’ll send it to you by email.”