Different airlines have different rules. The general answer is yes but there are exceptions and conditions.
You may have to pay for an extra seat or seats
You may have to have the cast 'split'
For example Ryanair:
Can I travel with a broken limb in a cast? < BACK
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All passengers travelling with broken limbs in plaster are required to travel with a medical certificate.
Passengers traveling with upper limbs in cast, waist and above, will only require one seat to travel.
Adult passengers travelling with lower limbs in cast, waist and/or full leg plaster, must purchase three seats in total, per journey, to travel. This will enable the leg to be elevated during the flight and reduce swelling.
Passengers travelling with lower leg in plaster, below the knee only, will only require one seat.
If a plaster cast has been fitted on any limb for less than 48 hours then the cast needs to be split (the split need to run along the entire length of the cast) If the plaster cast been fitted for more than 48 hours there is no requirement for the cast to be split. This is applicable for both plaster of paris and resin casts.
A medical certificate confirming fitness to fly will be required.