arcgis desktop - Copy .prj file into QGIS projection folder

I want a custom projection used in ArcGIS be available in QGIS. I have the .prj file copied out of a ArcGIS folder (containing different projections). Now, I want this file to be added into QGIS. Is there a folder where I can copy this file into?

The custom projection is:

PROJCS["ETRS_1989_UTM_Zone_33N7",
GEOGCS["GCS_ETRS_1989",
DATUM["D_ETRS_1989",
SPHE‌​ROID["GRS_1980",6378137.0,298.257222101]],
PRIMEM["Greenwich",0.0],
UNIT["Degree",0‌​.0174532925199433]],
PROJECTION["Transverse_Mercator"],

PARAMETER["False_Easting",3‌​500000.0],
PARAMETER["False_Northing",0.0],
PARAMETER["Central_Meridian",15.0],
PARA‌​METER["Scale_Factor",0.9996],
PARAMETER["Latitude_Of_Origin",0.0],
UNIT["Meter",1.0‌​]] 

Answer

You can use the gdalsrsinfo utility for converting the projection definitions from .prj file into proj4 format http://gdal.org/gdalsrsinfo.html.

In this case I saved your definitions into a file "prj.prj" and run this command:

gdal_dev>gdalsrsinfo -e proj4 prj.prj

Warning 1: EPSG detection is experimental and requires new data files (see bug #4345)

EPSG:-1

PROJ.4 : '+proj=tmerc +lat_0=0 +lon_0=15 +k=0.9996 +x_0=3500000 +y_0=0 +ellps=GRS80 +units=m +no_defs '

OGC WKT :
PROJCS["ETRS_1989_UTM_Zone_33N7",
    GEOGCS["GCS_ETRS_1989",
        DATUM["D_ETRS_1989",

            SPHEROID["GRS_1980",6378137.0,298.257222101]],
        PRIMEM["Greenwich",0.0],
        UNIT["Degree","0.0174532925199433"]],
    PROJECTION["Transverse_Mercator"],
    PARAMETER["False_Easting",3500000.0],
    PARAMETER["False_Northing",0.0],
    PARAMETER["Central_Meridian",15.0],
    PARAMETER["Scale_Factor",0.9996],
    PARAMETER["Latitude_Of_Origin",0.0],
    UNIT["Meter",1.0]]

The answer is: have a try by adding a custom projection into QGIS with proj4 parameters

PROJ.4 : '+proj=tmerc +lat_0=0 +lon_0=15 +k=0.9996 +x_0=3500000 +y_0=0 +ellps=GRS80 +units=m +no_defs '