PROBLEM
Rotating the data frame in ArcMap using the tools from the Data Frame Tools toolbar does not rotate the labels in the data frame.
This is a known limitation.
Option A
1. Close any ArcMap and ArcCatalog sessions.
2. Open the ArcMap Advanced Settings utility file from the ArcGIS for Desktop installation folder.
This file is usually located in the following location:
C:\Program Files (x86)\ArcGIS\Desktop10.3\Utilities
C:\Program Files\ArcGIS\Utilities\AdvancedArcMapSettings.exe
C:\ArcGis\Utilities\AdvancedArcMapSettings.exe
Option B
1. In ArcMap, activate the Labeling toolbar by navigating to Customize > Toolbars > Labeling.
2. Activate the Maplex Label Engine by clicking the Labeling drop-down arrow > Use Maplex Label Engine.
3. Click the Labeling drop-down arrow > Options.
4. Open the General tab, and check the 'Rotate point and polygon labels when data frame is rotated' check box in the Data Frame Rotation section, and click OK.
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