The Lewis Acid-base theory defines acids as species accepting pairs of electrons.
The central boron atom in boron trichloride #"BCl"_3# is electron-deficient, enabling the molecule to accept additional pairs of electrons and act as a Lewis Acid.
Each boron atom forms three single bonds with chlorine atoms with all of its valence electrons, such that there are #2*3=6# valence electrons available to the boron atom in a #"BCl"_3# molecule.
As a period #2# element, boron demands a total of #8# electrons in its valence shell to achieve an octet; therefore, borons atom in #"BCl"_3# molecules are electron deficient and would be willing to accept additional electrons to form an octet.
The reaction between boron trichloride #"BCl"_3# and ammonia #"NH"_3#- in which the central nitrogen atom carries a lone pair of electrons- is an example in which #"BCl"_3# acts as a Lewis Acid despite possessing no hydrogen atoms. 
As seen on the diagram, the #"BCl"_3# molecule accepts a lone pair of electrons from an ammonia molecule. In this reaction, ammonia donates electrons and is, therefore, a Lewis base whereas #"BCl"_3# accepts electrons and acts as a Lewis acid.
 "Boron trichloride", the English Wikipedia,