Yes indeed. Primary amines can be made using Grignard reagent. The first reported instances of such reaction was found during the 1930s where they used mono/dihaloamines and reacted with Grignard reagent to form primary amine, secondary amine and other side products like ammonia and mixed magnesium halide reaction (Ref.1a).
$$\ce{RMgX + NH2Cl -> RNH2 + MgXCl + (other side products)}$$
$$\ce{RMgX + NH2Cl -> RCl + MgXNH2 (side reaction)}$$
When dihaloamines is used, the yields are not that promising (Ref.1b):
Dibromoamine reacts with Grignard reagents to produce primary amines, secondary amines, ammonia, and nitrogen. The percentage yields of these products if Grignard reagent used is n-butyl magnesium chloride are n-butylamine 7.8 per cent, di-n-butylamine 2.2 per cent, ammonia 79.0 per cent, nitrogen 5.9 per cent;
There are tons of other electrophilic aminating agent beside one mentioned in Waylander's answer. Some examples being 4,4′-Bis(trifluoromethyl)benzophenone O-sulfonyloximes (Ref.2a), 2-Imidazolidinone O-sulfonyloxime (Ref. 2b). You can find tons of other reaction which uses Grignard agent to produce amines. (Ref. 3)
References
- The formation of primary amines from Grignard reagent by George H. Coleman and Charles B. Yager:
- Preparation of Primary Amines from Grignard reagents by Koichi et.al.
- Synthesis of amines by the electrophilic amination of organomagnesium, -zinc, -copper, and -lithium reagents by Tahir Daşkapan, DOI: 10.3998/ark.5550190.0012.520