Block[{$MaxExtraPrecision = 100},
 Table[N[CDF[VonMisesDistribution[0, 1], x], 50], {x, -3, +3, 1}]]

(*
{0.0065699445657434725994454209986633014972225550978276, 
0.065759044110016834719498414716497613321574175779747, 
0.20564469256531652001232187026473994135450073737055, 1/2, 
0.79435530743468347998767812973526005864549926262946, 
0.93424095588998316528050158528350238667842582422025, 
0.99343005543425652740055457900133669850277744490217}
*)

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With Mathematica 12.3.0 I get:

 Table[CDF[VonMisesDistribution[0, 1], N[x, 50]], {x, -3, +3, 1/10}]

 (*{0.0065699445657434725994454210, 0.011281889323008449016465152, \
 0.016107923474357193058325287, 0.0210983540862561413282222594, \
 0.026306670805056431497154380, 0.031790483694380358034179071, \
 0.0376124488909580429597147929, 0.043841159387262203807815762, \
 0.050551965200199534173485257, 0.0578276713748728364467548595, \
 0.065759044110016834719498415, 0.074445035735229374984836850, \
 0.0839926200247749571260022184, 0.094516113017898752435980587, \
 0.106135844740139079754445795, 0.1189760484864219467333907624, \
 0.133161851675682407809176805, 0.148815290611378985785552099, \
 0.1660503344857374974167467233, 0.184966992829700623067367120, \
 0.205644692565316520012321870, 0.2281352379392801936804270821, \
 0.252455795290335123135976931, 0.278582456097695423404503028, \
 0.3064450042385326754313744128, 0.335923525395006967297610149, \
 0.366847431566248773453300477, 0.3989973247972686367644852854, \
 0.432109898069595965244872820, 0.465885789192084127458345266, 
  CDF[VonMisesDistribution[0, 1], 
   0], 0.534114210807915872541654734, 0.567890101930404034755127180, \
 0.6010026752027313632355147146, 0.633152568433751226546699523, \
 0.664076474604993032702389851, 0.6935549957614673245686255872, \
 0.721417543902304576595496972, 0.747544204709664876864023069, \
 0.7718647620607198063195729179, 0.794355307434683479987678130, \
 0.815033007170299376932632880, 0.8339496655142625025832532767, \
 0.851184709388621014214447901, 0.866838148324317592190823195, \
 0.8810239515135780532666092376, 0.893864155259860920245554205, \
 0.905483886982101247564019413, 0.9160073799752250428739977816, \
 0.925554964264770625015163150, 0.934240955889983165280501585, \
 0.9421723286251271635532451405, 0.949448034799800465826514743, \
 0.956158840612737796192184238, 0.9623875511090419570402852071, \
 0.968209516305619641965820929, 0.973693329194943568502845620, \
 0.9789016459137438586717777406, 0.983892076525642806941674713, \
 0.988718110676991550983534848, 0.9934300554342565274005545790}*)

Only one value is missing for : CDF[VonMisesDistribution[0, 1], 0] but:

N@CDF[VonMisesDistribution[0, 1], 0]
(*0.5*)

or calculate symbolically:

   Probability[x <= 0, x \[Distributed] VonMisesDistribution[0, 1]]
   (*1/2*)