The former Lancing College replaces Hampshire team-mate Liam Dawson in the squad from the recent series with South Africa.
Leg-spinner Crane featured in two of England's three matches against the Proteas in a T20 series earlier in the summer, impressing in his first two matches for his country.
The 20-year-old could now be in line to make his Test bow in a day/night clash with the Windies at Edgbaston a week today.
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