The framework doesn't include the old seconds (or milliseconds) since 1970. The closest you get is DateTime.Ticks which is the number of 100-nanoseconds since january 1st 0001.
A common idiom in Java is to use the currentTimeMillis() for timing or scheduling purposes, where you're not interested in the actual milliseconds since 1970, but instead calculate some relative value and compare later invocations of currentTimeMillis() to that value.
If that's what you're looking for, the C# equivalent is Environment.TickCount.
I know question asks for equivalent but since I use those 2 for the same tasks I throw in GetTickCount. I might be nostalgic but System.currentTimeMillis() and GetTickCount() are the only ones I use for getting ticks.