Active rifting in Antarctica?
Unlike the East African Rift system, it is not possible to view the rifting crust of the West Antarctic Rift directly due to the extensive ice cover over the region (1). However, scientists can and have inferred the nature of the rifting from other methods, including seismic, radar sounding, geodetic methods and by examining the petrology of exposed rocks in surrounding areas. Also, of significance, are observations made of glacial activity, particularly of the prominent Thwaites Glacier (2).

There seems to still be some uncertainty as to the nature of the current tectonic status of the West Antarctic Rift.

On one hand, observations of radar sounding and subglacial water routing at the base of the Thwaites Glacier show some melting that Schroeder et al. (2014) (2) suggest that the melting is due to a geothermal flux that is consistent with magma migration and magmatism, they record a minimum average geothermal flux of ~114 mW/m2, with some areas peaking at >200 mW/m2.  Petrologic observations by Martin et al. (2014 (3) based on samples of of Cenozoic outcrops of surrounding exposed areas on the shoulder of the West Antarctic rift system suggest active rifting with mantle 'refertilisation'.

On the other hand, seismic observations from authors such as Lough et al. (2013) (4), match geodetic data from the POLENET (5) program suggest that much of the rift is not presently active.  Although several earthquakes have been recorded in West Antarctica, very few occur in the rift itself, and these tend to be much smaller magnitude.  Lough et al. (2013) suggest that some of the shallower quakes occur due to glacial activity.

The seismicity further reinforces the conclusions made by Winberry and Anandakrishnan (2003) (6) that the earthquake pattern suggest that the West Antarctic Rift is a dormant rift system, with a possible hotspot origin for volcanic activity occurring in the nearby Marie Byrd Land (1).

The evidence suggests that the West Antarctic Rift system is either dormant, or a very slow moving one.

References

(1) Winberry and Anandakrishnan, 2004, Crustal structure of the West Antarctic rift system and Marie Byrd Land hotspot Geology

(2) Schroeder et al. 2014, Evidence for elevated and spatially variable geothermal flux beneath the West Antarctic Ice Sheet, PNAS

(3) Martin et al. 2014, Increased mantle heat flow with on-going rifting of the West Antarctic rift system inferred from characterisation of plagioclase peridotite in the shallow Antarctic mantle Lithos

(4) Lough et al. 2013, Subglacial volcanic seismicity in Marie Byrd Land detected by the POLENET/ANET seismic deployment American Geophysical Union, Fall Meeting 2012

(5) POLENET 

(6) Winberry and Anandakrishnan, 2003, Seismicity and neotectonics of West Antarctica Geophysical Research Letters