You are off slightly on a few things here, so hopefully the following helps.
Firstly, you don't need to select ranges to access their properties, you can just specify their address etc. Secondly, unless you are manipulating the values within the range, you don't actually need to set them to a variant. If you do want to manipulate the values, you can leave out the bounds of the array as it will be set when you define the range.
It's also good practice to use Option Explicit
at the top of your modules to force variable declaration.
The following will do what you are after:
Sub ARRAYER()
Dim Number_of_Sims As Integer, i As Integer
Number_of_Sims = 10
For i = 1 To Number_of_Sims
'Do your calculation here to update C4 to G4
Range(Cells(4 + i, "C"), Cells(4 + i, "G")).Value = Range("C4:G4").Value
Next
End Sub
If you do want to manipulate the values within the array then do this:
Sub ARRAYER()
Dim Number_of_Sims As Integer, i As Integer
Dim anARRAY as Variant
Number_of_Sims = 10
For i = 1 To Number_of_Sims
'Do your calculation here to update C4 to G4
anARRAY= Range("C4:G4").Value
'You can loop through the array and manipulate it here
Range(Cells(4 + i, "C"), Cells(4 + i, "G")).Value = anARRAY
Next
End Sub