Here's an efficient option that doesn't use the clipboard.
Sub transposeAndPasteRow(rowToCopy As Range, pasteTarget As Range)
pasteTarget.Resize(rowToCopy.Columns.Count) = Application.WorksheetFunction.Transpose(rowToCopy.Value)
End Sub
Use it like this.
Sub test()
Call transposeAndPasteRow(Worksheets("Sheet1").Range("A1:A5"), Worksheets("Sheet2").Range("A1"))
End Sub